curve #1969

y² = x³ + x² − 860412800064509124151108089665x + 309454963096823539740599704296592217188082400

a-invariants: [0, 1, 0, -860412800064509124151108089665, 309454963096823539740599704296592217188082400]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 1291457022988031677001254686104164327540420658465259628208091402180
discriminant (Δ): -603114576317557433493337841429111290495286375579433065138749162495066267327889655912750000
Faltings height: 16.0525
naive height: 218.4099
primes of bad reduction: 2, 3, 5, 7, 17, 67, 97, 131, 212453511640458091434048105692433140388925135524806512273
regulator: 3037761511851193656.96684436553523362631684723855497152182944204570508720051767
submitted by: Ritik Jain
submitted at: 2026-09-25 20:07:12 UTC
last updated: 2026-09-25 20:07:12 UTC

(203453030131645, -11950854806147377605975)
(1805142484384555, 68105911282283094042015)
(13261251204348777310564345/2434336921, 47633829122267335456586599475380223475/120107749345219)
(2142067437997384765/5041, 1623186507199408130373509745/357911)
(65929830405143854345/92416, 215277301505805589254959566875/28094464)
(16509431819049683102926642234266715/1000732848217451449, 2117998400410917429256936393496990791006737265754445/1001099473701525849860501293)
(7311216764385025885/12769, -3067089817346466225750852615/1442897)
(9692471153823436495/1681, -29806944106441730700131630775/68921)
(782032066526625948145/80656, 21772819863360607449309018224625/22906304)
(551064705271465, -1629395192656034752095)
(11259749446460784745/256, 37774374300132071621304604725/4096)
(31192443823272055/49, 1522297090305946098178425/343)
(47238588002240145/16, -9811964663616978934329825/64)
(31714842202249823155/10609, 170874256253465585961132323625/1092727)
(2890389719012089529305/3794704, 72426750373290115190852075878875/7392083392)
(3605694509481792595/6241, -1124365530096462888463784625/493039)
(678568418623795, 6168978700066229630625)
(11248640995452024334021600/24824838481, 13894026446625813107299673453371280880/3911376726227879)
(25585726887165789315565/54037201, 1138342856307145368665249561957055/397227464551)
(-36807141953478739985796500/34336460601, 588369210685184702523301971877436930/6362580485825901)

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