curve #1973

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y² + xy = x³ − x² − 1395049016570522506364481093289x + 580400018165462671445665071524186578657361569

a-invariants

[1, -1, 0, -1395049016570522506364481093289, 580400018165462671445665071524186578657361569]

rank (lower bound)

≥ 21

torsion subgroup

trivial

conductor (N)

94458606071860005404785166791135853414182327226136203943493390475248437637238

discriminant (Δ)

28234100808728797229953732612254083331152137704651904497180012266338683119642781941399494972

Faltings height

16.2860

naive height

219.8451

primes of bad reduction

2, 11, 13, 23, 79, 179, 887, 977, 20959, 2807737767827, 1531718308878593200335776535006041020865853841

regulator

1824677472742186640882.7889609727969829865333775358795984472630775673140524737931

submitted by

Ritik Jain

submitted at

2026-09-25 20:07:22 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:09:30 UTC

Witness: 21 independent points log in to add more points →

(3190439330328126090504999311751199560/3598744232849599678321, 1372445200032554493243364799919840424501888263351627857/215886990812981644847732176287881)
(85089536412344296/225, -34896890939680145108249401/3375)
(74675966824381053472/45369, 506161698953599106992405237379/9663597)
(6674201034120958744/18225, -26797783185146952666651746017/2460375)
(29305134440997898/9, 4720025857647536184113075/27)
(4637661344019831, -306360907555874326430696)
(13342697719862182052/289, -48721941695241992615936714809/4913)
(12564992325033892285816/2732409, 1365546865726810969504789160056291/4516672077)
(-276724175508444720/361, 237538500166145426864830603/6859)
(-123826935287110147976/178929, 2637555815794254971662219323743/75686967)
(80997260924865412, -23049396428648164724710267)
(-401347126328934, -32797105331251764268615)
(49728570965781199240/301401, -3116449493959389368784898538683/165469149)
(840808097742922, 1359314013395002465653)
(-131495027743447736/2025, -2359970110278094074491998853/91125)
(-70132876052517870429366/74425129, -20886616575734992723895107871624765/642065587883)
(4963001626174835771207488/40009200529, 161896815624565389058707784138694241801/8002760317412167)
(-721055766152362093060262552570015747611480718988566336/540647491836764786391864715892541543225, 104190110440103769293986227734875807101320561853811977351609286037123115459809533/12571042331813995068068511770371597356270483651812287945875)
(-690181263992806739360940797246363848557982594615064467580278726997/640750096723463143137560948466434389310116468980801, 468208190765519530203589108050853641220314617350084300118283515225390646586718815699035030334802440/16219334127960102186777058430720467679008592193447150419297057701768209711201)
(-3725082685623005479000275798586037773328032004401956/5078567703372843388367546266786440289, 397951936528626123045197173102976339095692338987484387315000266605887913728217/11444896504664540273261631380555023992432872551615943663)
(-24739360738772625335582821043547214870842602862215433291393694077803191300/19339212205001653500414593800348144049529570698760462195601, 44323035521803732471161254000018941253171184555164603517404926909894211650448710066627164977480413445377115713/2689417139434358655717111668544217484203395438634761447822064927401056694733615595022151)

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