curve #395

y² + xy + y = x³ − x² − 1571436138788579721131230519678999674817868532078561707x + 745728645244690014891125566886054009886463789156281759801829847987045667940220539

a-invariants: [1, -1, 1, -1571436138788579721131230519678999674817868532078561707, 745728645244690014891125566886054009886463789156281759801829847987045667940220539]
c-invariants: [75428934661851826614299064944591984391257689539770961921, -644309549491412172865932489450120458563571494066681648218117058900147854171381217281]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 1606128851319113781338598344699617246184318747300785693780504765923760131894092361926484435226700027439963578832453553533656857770
discriminant (Δ): 8113398369718691119421954154704599870628390245687158566363676758657802036863710381968341196323156227070347002510325828954325105493690216640422894123776286720000000
Faltings height: 30.0530
naive height: 385.9884
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 29, 31, 37, 67, 562214432877765374330329, 32155840277224765434666491576321845332264089, 26028959252280369865313058197486819425881612718309
regulator: 938033216495430790231582000705250.1439003628088938214717873966185324946644031378961386375342208
submitted by: wgxli
submitted at: 2026-08-28 00:51:15 UTC
last updated: 2026-08-28 00:51:15 UTC

Witness: 28 independent points log in to add more points →

(9471384341054712676308813126670218257391535783549063/8455897188058941172476324, 486121392618956187136644690413166942473623526717489789797414733840818813693027/24588924919743556042598482763043857832)
(10925167993903726643301055597, 1134723702907179649372025118363306209916326)
(4036352452312455653355236275747/10201, -14047248847203198959170990890590865555615933374/1030301)
(2135857343570798380486973263/4, -61386949770752880358427333877832141192517/8)
(-275725311879785168159218997160785184053/203537224801, 1809970535295798625590098015356840361633834468200450905526/91826022506195951)
(-780116223691187205401565653, 38689369451013387731585007847783168678826)
(35238169531748521994326283947, -6610719615221200736253802976740106607577174)
(21639169417103142129683046155231279261081587/48066545485423921, -119932503006919890733661096457830904340626543125332081159200991106/10538149760056002710709719)
(2686447457658406278917735951958517072711987/1650913997736481, -3352249629729042510914007419252430402219379683511907683003078454/67079014695103961299121)
(908231581941253300273520238772084496179/2478549584281, 57758772137834174660945391214401975783853888464760742029442/3902082231066533821)
(18219284729627674892556671556257239831824097/45313104300825001, 129013111408526090275249441534501578900046410966547276729067536174/9645743825823137630793749)
(6653110812079049269152252468707/11881, -8327916056683409918172207760312445796384604046/1295029)
(11284128465168434886199710067870863887812583/14118041974280689, -958652347625684672125737152462986215712235770919155625127145162/1677496810663461747303863)
(-36686422862973936166789650112133/78961, 822917877124384103513949929240964586230566255866/22188041)
(2622282271713984242047698347, -121065055850165538906565521242663385721174)
(731531168183460111639049840121491564567/5656681910884, 313985562983427770713632100952170888197586312948089295321831/13453727809844466152)
(77524947346790938823415070123/9, -21368430220457522461922676082048352421546698/27)
(87941566251695215446918966500669513952415547/6837399443267761, 820909946199074254465049092693480133888082061499786211757486811834/565374775645207840924009)
(1323924497144784154427635292515561331646773278807/1065744807569356571281, 927481788263911657141919443411306601045126777592223867078482756805299154/34792035523926323982354686740679)
(195632868364168614022819167816603764049667784587/4475729040802588321, 86494002702945666424735595518883291969160758364450163022492058965929994/9468816056083705902113728369)
(183959025058098651027341437242002805159373548097/89967073654966697401, -66547344360855741004871628728858508926001537433972004063063605332361024/853346460998653875008113424851)
(522167601186412329485594279825646695442451/653914244632009, -4461961302483368575454651335463895269151071246525967485388626/16721729623425842249723)
(1043112223736381423310365634222654553363/356496167329, 30991229916664218022070400507058056749617043534789015893442/212854236115628017)
(1454129024077231695922889005095261296941653571441607/1237612105568165321417641, 31438240692866866351998203649912152113589865072363600991234664477940883104514/1376818912761255356511359352256615189)
(1983790026201047020951092602322680964952554362400448663/45894441426248106610376329, 2792948002515860930959862300222857823424393743935164631674354734729777351037048542/310913895923210012870060203185638482267)
(33007599088148997094881340157665514798924770793777587/23334989887704352400044441, -4146490665954064198601963800359394672407644329674509317562192460164591356594174/112722711115697447724931086245207395261)
(968473110472751251461144472064829629603237/389016886167121, 849680856128956146886458034828016044992176925070307364009880156/7672778833502958881831)
(663423012872227641253536565314101687013101037210179467/748521911915690559251209201, 143624787316409092319391537917341263644233420692571147519261102054171854048803206/20478907168190136984463269782080038522551)

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