curve #1883

y² + xy + y = x³ + x² − 3874636681786621682862301394748669661445x + 92104320408916058733797120705434107205731052713500724197771

a-invariants

[1, 1, 1, -3874636681786621682862301394748669661445, 92104320408916058733797120705434107205731052713500724197771]

rank (lower bound)

≥ 25

torsion subgroup

trivial

conductor (N)

1959032268792848001636268300560143641494180786728840729128766414724159224398815584110044565134149920866

discriminant (Δ)

58082729784920213331130729941349735852649264287049797744699795736042690485799111313332303264375148104213038031140503552

Faltings height

21.6113

naive height

285.0794

primes of bad reduction

2, 3, 17, 23, 29, 31, 37, 109, 6101, 128311, 19827221775815344873666247, 14838803680115940062391169021516209969268321563453744109139

regulator

3446274458998975503782780893.726684351192668727400131969820254812288197579611967781170250

submitted by

Ritik Jain

submitted at

2026-09-25 17:33:56 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:42:44 UTC

Witness: 25 independent points log in to add more points →

(539872504287601451463/4, -11392024081037323943023989768481/8)
(18357223275234322126995471/7396, -78627628680336744010741697824721856319/636056)
(-923022601475069738083/16, -22503858206278642945688893512229/64)
(810624013608287927637, 23013505235331252834805474144564)
(-1479947766411614969, 312786410931598546426996317212)
(-61744921912677575001, 309749793908034475152892337404)
(219134436685940905707359/25, 102578188728323784151880533288290188/125)
(6450866079503386234413/121, 256250539996857938242762865592194/1331)
(297710416134167751649/9, 308985914372505980864437317604/27)
(-6232186580924138371915373/97969, 8735676762024203795363036631547254404/30664297)
(54793169168319579687, -210489327847893940862269596836)
(-28505683554466000027689/529, -4623848307148570243573410503788252/12167)
(152510482701889403436631/2025, 43462280076139169312128960757936644/91125)
(104194571551246689821, 905305190597996954566377242846)
(408421431282529730047/9, 2662852051305766555376878100468/27)
(-67238291508079673171793/10201, -352954438065568346587638543715501012/1030301)
(-63660357961620765039, -284205015056115586945686079598)
(-35793199195875652857, 430038829139766705805260076252)
(11921577842588767028871/361, 87818656416853275124798848882124/6859)
(-32042379712020132156772977/727609, 261360072697949203857954224083654649836/620650477)
(-67508598115824180201, 214502204073326128532695308604)
(49415745327348950817722320244471/1487965711684, 13451945747970218250094585403268260341534903033/1815053310357800248)
(130580044742232873202284195944070894964929249/3920899545863210318981329, 13420643425200127992181413684917412058167583379232591112910064446/7763875698475244133537494647479738983)
(347893943631585747879127095767203/12706066606249, 3663391866493886762246904112400506655947603734112/45291498663771116693)
(-4055710578913768993109571840148823355/62621476969322896, 4186824110980672836789145817639738795053823754351418007/15670575991312046494773056)

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