curve #1946

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y² + xy + y = x³ − x² − 8979997388703130972379558515674512x + 328794408239606618900762149983614952811671442231411

a-invariants

[1, -1, 1, -8979997388703130972379558515674512, 328794408239606618900762149983614952811671442231411]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

389472087878281367589811764849776009941810088048600077540561279038434489913072725924130

discriminant (Δ)

-356079310906355522889430332430579480511427021854806071471929014878084057755199051050654246181427200000

Faltings height

18.3383

naive height

246.1622

primes of bad reduction

2, 3, 5, 13, 23, 73, 101, 1199087, 1963440652836761336882342599697939, 833777044007518853119779549713831984887

regulator

661673681338779736860257.536134977245455222182547854265488971087276722738274787370554

submitted by

Ritik Jain

submitted at

2026-09-25 20:01:16 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:03:56 UTC

Witness: 23 independent points log in to add more points →

(3145786008614339346108150121/14891076841, -161096867506851542879273577460236695980099/1817143215830389)
(7431039775633757221/121, -3977379185447586251435848061/1331)
(927364329780171061/9, -602231388141501453434816293/27)
(2145511052010175600189/97969, 366225558759139079159105500184873/30664297)
(390268633368713899/4, -156239313778133650853160803/8)
(-20285987890712419, 22419063557077996868177809)
(22721479029032365508278625777815375069/5827964283937996209, 108274895888813389039788097679528019177975968870175287863/14069391750306435202493787927)
(52314824172429469, -1478096942982658986692719)
(1187082193514643829/25, 384329811687875156934656557/125)
(-58359625378257091, 25575374951600239643066321)
(-85660854467063969, 21667209892750002365921759)
(7037529308233471, -16307849643104764948835071)
(2231649222070046689/49, 1296145251361483610486958707/343)
(41560670701432049, 5231347579430293791747461)
(50363490721871621, -2067955618851593727411751)
(1241366973282308611/25, 288407773049177178684915919/125)
(340569335995251499/4, 107757276419861590807193197/8)
(-10413475235913888890931925775386291/1755036041852619289, 45434503703933998817474446786996428138343839001161533/2325032668858806101793491837)
(-273376964294350928042058967751/2869591956169, 86912329293827303151333670846193593620430547/4861051469054855803)
(16657865975674566511031673965109466489/315212967422254188169, 7550415351910575887736966461406814941545447013938281273/5596366048398715929738514668197)
(-3698318966909057702228557013656305521/46019476163471890689, 7196803609867426872647711703692226819051621310038411343/312185340846423302017570891137)
(53368885967290342234341769691393621/953373732672970921, 1148284208933274612956639951412485018464429487967301/930882301108878735411640469)
(-40471893867154583481268626627331822247183159091495053941454925325373820515610785495871217996273823677240619596962839473998354885961544723117751945859/1125972428054025456662020556266142779901772390157865815827282192480897417280486896755787730862018775740651416085818913585944431467761, 29391171271526600743035045457700864434814850013106060542749552209320779355843440569525968271040000637106112983084663416584422729427836270091266084237191771970015570236955179733731782851080845828530802069112549172839173273481/1194790151090245892070053729849090211857396082608199897774900333187277425879162770695969744226066526011671657071209502504463009069121277397923771095677814755023809047731769025374940082421512669624009)

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