curve #1860

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y² + xy = x³ − 312116498044431103449067796618358700x + 67490359782208585066323454846394949810594640241690000

a-invariants

[1, 0, 0, -312116498044431103449067796618358700, 67490359782208585066323454846394949810594640241690000]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

1156979327301776831857746318066418137028261781201741022082482337927508861204420910

discriminant (Δ)

-21794663497523704700576787588512296816288430469329769398184322593401946195594103090218809567360064000000000

Faltings height

19.2410

naive height

256.8108

primes of bad reduction

2, 3, 5, 13, 19, 31, 43, 67, 11016518413, 158693111103922475370370469630874742561792731811671547655452757

regulator

43845154426915734317268.1054277680775755668970362342511598547772740257796128874670684

submitted by

Ritik Jain

submitted at

2026-09-25 17:14:33 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:17:02 UTC

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

(54900431771747521150, -406762812098137028295497079950)
(-209004828765335956674025443064039300665695000/330900734755727675365448521, 676870907593341658629935687304640982375314562045615025916259209700/6019308430820962677546540664414084666181)
(260927933341252681400/361, -3213513635101416341352656743300/6859)
(19498723304687222600/49, 27228852421048030195841555900/343)
(19471610424940889756, -85886709097925114696658628348)
(1402493986136017400, 1545457739307877047764321300)
(147790551132490730, -156813707010721363824649930)
(638226456669075770, 358134132121689309631981280)
(-619141170872945373850/961, -1011941722810999355269287445450/29791)
(19454034246668877200/49, 26908072771131717692821258700/343)
(321624837981967960, 19381193803723805704901140)
(374723407058670860, 56131770086760878905280240)
(287167911692917400, -39267496481426718666678700)
(1927563816682154120, 2574438505384503085288375700)
(1791408668242535000, 2292869895144213426781063700)
(3178677762146415044391400/13995081, -4774650089031525661069379470174374700/52355598021)
(3351388791934211863640259920/19996505281, -398771568549381634312726550646531443502700/2827685815280929)
(11601127361784869275/36, 4182195253608559181492028925/216)
(14942197165668499710945659373211307747039300/49829642209802881463325289, 10321785825430445657029491233216780858129926910003155646471915000/351748013350378419518699275411767238837)
(-150564851779264690334890091260810/298992894370921, 1609897157644014405841646128570620732748373851150/5170009022647181459531)
(12685777661093469297352857161039480773400/39510036449590667346961, 152466247767999172429193444339638241081633823049304433451700/7853461978578329929527023229881209)
(184228048503090104950704048004623771150994/823746979076260680543249, 70424500796648707444672452415006935471969505304014725990508256/747636941861537755027330960216823943)
(24466180937258429071087447358308947367850/84817595774495488481329, 943847242968634705439899802058747989390785431471848282193350/24701819093444142928175560330511017)

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