curve #1921

y² + xy = x³ − 1086750289534747727483801311783198679020964x + 435973165715323898311705750809969552813996511661336976727731984

a-invariants: [1, 0, 0, -1086750289534747727483801311783198679020964, 435973165715323898311705750809969552813996511661336976727731984]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/4ℤ
conductor (N): 31023331291622976051227194580729790167205619926
discriminant (Δ): 31391848322214844147689545020197141229274491206455128154118457320503704791204918804998073398465359587463871613420496710795264
Faltings height: 22.8821
naive height: 301.9889
primes of bad reduction: 2, 3, 7, 13, 29, 31, 43, 73, 79, 83, 89, 151, 199, 239, 263, 601, 617, 1433, 3449, 6199, 1607849
regulator: 312848498549.62405624139280925577340874383690316899070741394065
submitted by: dujella
submitted at: 2026-09-25 19:11:32 UTC
last updated: 2026-09-25 19:11:32 UTC

(667212090873280716424, 2811468741600154868659805081692)
(588300445738899279592, 496738531576486238655704034844)
(640878480652690741030, 1650227478438617514410537429218)
(594914072761535795656, 61252759091705020914823536412)
(638462258521963853092, 1543723151978346502319214760144)
(611110705367872899304, 267524019061985430016982751484)
(594950966257051623880, 53222697163458916334270893852)
(716616869926847885656, 5020041299716878281470542342412)
(627762722675286133960, 1069751374718071593281800264732)
(510340803979604535780, 3778525680405340851280110580752)
(617601639147843518920, 606053623188294616739131272988)
(610092172393399908808, 198061390862962920112854267676)

found by Elkies (2006)

last edited by dujella at 2026-09-25 19:11:33 UTC · history