curve #4125

y² + xy = x³ − 30326382791435754843013396863384968720259562774881026x + 1974620385898414358174036745594922329633068151571885455372512908629292482834756

a-invariants: [1, 0, 0, -30326382791435754843013396863384968720259562774881026, 1974620385898414358174036745594922329633068151571885455372512908629292482834756]
c-invariants: [1455666373988916232464643049442478498572459013194289249, -1706072013416230005462367750377512453786345231655073607605568900914397224960663057]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 122476517289985637066269292234016565764186430781473965549569412350148532718549910 ☆ record for ℤ/2ℤ torsion, rank ≥ 20
discriminant (Δ): 100592470956274823767495656980552629164170334997615219635536514321131394168478950205264375157549127228600712160004788845803016011626606392760947782340680240000
Faltings height: 29.0915
naive height: 374.1452
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 53, 67, 83, 89, 101, 107, 227, 241, 347, 509, 839, 1307, 1427, 1787, 2341, 2749, 10613, 21529, 25847, 27983, 47279, 51853
regulator: 4763992101874590621710.50886648094775760211912773709976004172265885076442428208
submitted by: wgxli
submitted at: 2026-10-09 23:07:51 UTC
last updated: 2026-10-09 23:07:51 UTC

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

(85399971486515325657849466, 87082721366727179098517149187915138242)
(86198553134160165301362316, 31650331370761301541362366866171645942)
(86310712253774162156011566, 10183733870645821208100541388378650992)
(33680038625032679996612416, 995706495710199615946879276094289698542)
(55239524196988701658984816, 684078644650665609116905644849049113442)
(118570148755389149570311480, 213963036276552660897046714646201616634)
(123259660639430125985854600, 330572002564677793127927210202167150734)
(129863728348394267823035866, 475837699536862162579452596022768645442)
(14191994216429418164071216, 1243819514474808647371393305191464682542)
(146230153295749455482216080, 816618538636808733626724744280869737134)
(-35244731483609075680501784, 1731959847275415648511215319718516543242)
(164160156504126205375304524, 1191686188816968903584062898689007069878)
(172719383395823077563857566, 1374492041958147329081557057760600145442)
(238480515791265383275616974, 2881919664986673252248891342058577301218)
(256221612807404761266996166, 3320417181075423901532706123097336468792)
(308254189865187706252009090, 4681548669773413922503242874132253438434)
(472472287745421399694690066, 9649676851628083720957265695612836705442)
(1166022676313118716664868216, 39394773223257651983764523048838836506042)
(2413300867888237312672458328, 118253554106863281859234725752030375766862)
(35507743623272659379565784/25, 173725285744717019281891047958871811644438/125)

Commentary

2-isogenous to curve #4124

last edited by wgxli at 2026-10-09 23:07:51 UTC · history