curve #3825

y² + xy = x³ − 345937228903231202467304723125095754860x + 2456005569524784582714002620373880155893602307078752016272

a-invariants: [1, 0, 0, -345937228903231202467304723125095754860, 2456005569524784582714002620373880155893602307078752016272]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 1669216171233312020362546059902352622250158945767442781520602685033470881912751468781463290
discriminant (Δ): 43740371997171235605565776190517886702263859429095691918702389138080257954895854932753893810983384086410790400000000
Faltings height: 21.0097
naive height: 277.8316
primes of bad reduction: 2, 3, 5, 7, 19, 23, 47, 131, 110813, 28065687727084151719, 24292130706800258664580285591, 39103054900077738653108296393
regulator: 25109180030776044332253459.56598040940777053119861458864375109280818332922822606350388760
submitted by: 7fff-zip
submitted at: 2026-10-03 05:21:54 UTC
last updated: 2026-10-03 05:21:54 UTC

(-8848350045703139976, 69456552993062161585480990548)
(-14651303113021303656, 66176869353854513255962816788)
(101069457851076189534, 999960198225601775791633078608)
(15362754672808700244, -27699919176173997955683799512)
(9359109989932742784, -6175188469083255248924855892)
(-4117566031835659848, 61730173310117845957613978868)
(15322076758382573784, 27434139699064801202619057108)
(-389266695535661766, -50898019867583918123879396442)
(-734789852404564052916/121, 87611937794950528928048449873968/1331)
(9332279656292719584, 6354865302014845809440375508)
(36057654575835087384, -191996980839906308472864677292)
(9878601387668969784, -1627985232435004972476554892)
(8919936173649154734, 8943412120061281943907331458)
(8656662927848461254, -10490708884487162425815839382)
(9034643955180820284, 8248442498705245449753940608)
(403607248854762633201/64, 11733685946653917086351430429771/512)
(9057633179252848704, 8107267341156308538971328468)
(13708418642541145512, 17024964317149353114430166148)
(11701683471367427184, 3203446045589448295546247508)
(19814663010414006864, 58146592239696352870398395988)
(9905331186702692784, -1118087893223534583161630892)
(29747634843696358284, 135976178582946662174918050608)
(11918323884760373034, -5095994568017032378483591392)
(1861729544181464226072/121, 37072557229483239478874433545148/1331)
(9879382665039059784, -1615180507781682042104804892)

X1008; T=251/63; 2-neighbor step: yes (Q has vector q=[-1,0,0,2,0,1,1,0,2,-1,-1,2,-1,-2,1,1,1] in source section basis; h(Q)=12; F'=O+Q-F).

last edited by 7fff-zip at 2026-10-03 05:21:54 UTC · history