curve #1825

y² = x³ + x² − 19535434198889703571837970065664831607303559505x + 1050083166374111347320128652662363470276826587824475277744332819122003

a-invariants

[0, 1, 0, -19535434198889703571837970065664831607303559505, 1050083166374111347320128652662363470276826587824475277744332819122003]

rank (lower bound)

≥ 27

torsion subgroup

trivial

conductor (N)

24273927005200623609042071279817166909776388569221759859798444778671159521245517896060621971602028924589644692725080

discriminant (Δ)

788232218046792215524739361820696253708067619768492881442581524217481443938497539307396901857197172271625934191836558042881522887060000000

Faltings height

25.3814

naive height

331.3793

primes of bad reduction

2, 3, 5, 11, 13, 17, 53, 136111, 89977517835643, 1894699524541304236229, 2556267359021606590798787, 26468182067627152874478812308612921506275197

regulator

5275759349527887600713205686636.4957239210887924623768114508730760523378524566979077236332991

submitted by

Ritik Jain

submitted at

2026-09-25 15:25:13 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 15:35:36 UTC

Witness: 27 independent points log in to add more points →

(73293667278480586368991, -3462704554266859790065979638992870)
(56017940546682582019111, -11468793031921997166632378139342630)
(641634543739020301213573440161443/43425141769, 250233898588398632966959790729367176515068862223850/9049235017816603)
(3574763966572053485957122369/45369, 320155885307115622219389181540853095250/9663597)
(-52523419517004947616833399/5776, -15376537614988700118045621673800340859475/438976)
(-5756752620444677022236543403460912861669187633381/136664022071567936617266169, 67749330803955318174456684734703638670011460256241426002354443815404666950/1597648724538158425546683626014081032947)
(-1987943552609969841321548981/12769, -25729928843748982958459061125461800402750/1442897)
(163577985025997310433955281/1681, 578857503722458557767905765361599961550/68921)
(643803642616131153723675166/5041, -9042090640418458994054559353084375954625/357911)
(-41076631542867194888249, -42228246747488313124092515213948250)
(1884056774025834331116001/16, -1251646250185033538262755710749186105/64)
(2246146000553351660721799/49, 5433129654405850312365349019062478250/343)
(913349793854145240014878, 863209686277185607140251783370859593)
(876121483976833267083847327/10609, 20576572343056563609521754619408669014/1092727)
(178210578526935872687259414646/2134521, 3185067101349228702297679398873729297890375/3118535181)
(489904782447374413261130353/6241, 265744306744395157234567840114464447438/493039)
(86524742200951141611886, 2748622274101279470678547294199295)
(2431901502892260133584918117739/44662489, 3628770353925604704837353031310757647439115750/298479413987)
(793775952887595159079741614332161351394920454215973512969038048770926165039303/10195231704600208806677218619338682173687424719402793161, 33497445700533314447327948683828260060292783842991127514311219591993651580821470758725704101182745402545541778407102/32553347220717831336061012013524955373703004089749701312549151176929878426587361659)
(-10765440468377755641549115096914669765012772688169040725004475021/568331426099165707508592420328397525721529, 16107359953390797996240437894260563294516354426246369610455894344087720263204793791127958825308550/428452327862470978715525466288401884458226079813797651825011667)
(75296702499987310815446286660370145583498383235891693059485046362989583630697731401013382838577627796163210662983672291050919/2209988508649529341421424506749423388387354737472478512411596884271346557115705733893241415268794857169, 67653277728012015169302843593995795839603311512752455650359026431225679790902016863242179135458820177052683569408654031610731883106073101403485027837852815390250572463872225342931023082250/3285375568509785500555791618553201151700760940515426835154274555384653197301006152622729318536911042611598662770083410002282970376776178591989960035411303)
(147525350656156814588089599112436750020601423818712267174531751011619/1782381204539007824064476160071939850360265969, 31986744853239616389956504601314378071679373835530211673977935946645241168120905505285511112948729650/75249027351900906156724826535194069768484786034306089722185702459703)
(-439396310346506170051346898637420916707253042981703913729082655478737116706397631/2763941631862238270563199849593683613022892009759829076169, 1706825908279238847072023131578679747177130867771297051763617947935893393053718907439801629376279543992781583746524886450/145309263392818687603848617473200529519974024153964080174757443049720012458325179922053)
(501110069008414532281919446896714156059951811407969585488795338056488878812206294099963580305695649763759625637443721/11804908628102598924353075838280081482498237283133825208069019777799062874682587077686137901721, 22115558952833115528322409823205084136516346710237906693271024823486745889735823009306437086850579325748717892624637266140310051808502453848650500671668166616566077544734129750/1282608001378124054531765806737557843272624611086333304815141540836750193298632335873342032621793722039725008332130613569462658720486329393981)
(602983028289781073595279644501644999661646716495373866536616369285588092914559/7739490364886894038356470017177001006584439431207572769, 21410481701873881641539384842137122337256152988941838421938307160065998614268669904434569399656599292340447945532410/21531215408825505450352974286152231600130323985064264503715865469429826840117137103)
(20951830633598028017153588015249422809934252561274266536951194778704950860439/334901381225586301344550577152508390619915371289150889, 1653430523071539374843222957980474262432616551439684824133563659007232579772011837786244736736779370691186200358050/193809654809702695747229960450389840397125055851241160282496672749974207170999787)
(556331458694510957764038413822036942994175840218807062236129108542215245193889106395526845980172067034519253208892699011/6326404252077716431290801514201021836971452689205383301826206682219987757087338758425955010447761, 55599754409789168929499956635535077979152953297819855497766126513615783762981512233292457202041238842050979052512446578638545188874598533279403720260633541600445582624381778943250/15912389810807954865978160325179772239998239700263987257401569002481283455402509260399624205211100003684563293374532638125675641686564911539054009)

Commentary

No commentary yet.