curve #1966

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y² = x³ − x² − 1164629707839590025636491065x + 15147197885324821326110064171938627845981

a-invariants

[0, -1, 0, -1164629707839590025636491065, 15147197885324821326110064171938627845981]

rank (lower bound)

≥ 20

torsion subgroup

trivial

conductor (N)

405414411986134846452214114346456137113006720328862373295747986408

discriminant (Δ)

1981188437917300579244168905261943063993052168029240515585150615698872244750058752

Faltings height

14.4129

naive height

198.5802

primes of bad reduction

2, 3, 11, 13, 31, 53, 59, 89, 730573, 69428048449, 269944042120321970074638341547492601429

regulator

3955825603509920416.18321250709861554596319493669371327272572276760832767539796

submitted by

Ritik Jain

submitted at

2026-09-25 20:07:04 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:08:39 UTC

Witness: 20 independent points log in to add more points →

(49007981827612497/2209, -1570986250023328016965306/103823)
(-1087022527118115/169, 328611935535392197843198/2197)
(1124488141982326539197624261949313134003459/45754682951396675000822683489, 362117226776401400115148317092313040083216587443015517884220018/9787084219259224464424168391117779124334737)
(-176046078686202195/5329, -51562378848143644414583078/389017)
(157541531617007643/10201, 29939680833428594668349338/1030301)
(1663787210228243689/9409, 2108731834251446202780386262/912673)
(119896423692471565449/687241, 1289378259439883395583643556318/569722789)
(169350957449463125/9409, -3660864609235906030062918/912673)
(3881601348010606717/2601, -7645463192570351196316890050/132651)
(38449730452746753/2209, 1267929445519624859089690/103823)
(4288215023732579/361, -374995299439506497827842/6859)
(594500068709678805/27556, -36273590620140592776660389/4574296)
(1828189184533986691/198025, -6343543134966917934674734686/88121125)
(561868586741585/49, -19705149549251222740662/343)
(1817596950479444/49, -52002596239306922722227/343)
(1016475630583045/81, -36511089486606529151786/729)
(5283144541875164377/292681, 394433269872845649677229570/158340421)
(-5066331235565003488724630631/286198524264409, 841632333651997065074949952227826456283182/4841735772986285609827)
(3049967875858062186876413089/434018763935689, 773077470450231692276775637751605819133298/9041963689267589412613)
(1072294051145910651818024632119825/62500679347299997456, 7264677802884138796963444390929385574318307200239/494113940491164244274604776896)

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