curve #4630

y² + xy = x³ − 537696860322492459000818098398744493445x + 4778995881945617226592708368864999074055175064513493581121

a-invariants: [1, 0, 0, -537696860322492459000818098398744493445, 4778995881945617226592708368864999074055175064513493581121]
c-invariants: [25809449295479638032039268723139735685361, -4129052442001013283814814204642578657031730158824368057616585]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 1654931758598356861737505042794803450985219219546468670571684358
discriminant (Δ): 82936533658166240973186938220473717783356594257787454701401131773805434907233332635871795602999700017173968980017152
Faltings height: 21.0914
naive height: 279.1547
primes of bad reduction: 2, 3, 7, 11, 19, 31, 37, 61, 137, 257, 283, 631, 977, 1567, 2927, 3371, 3989, 4597, 5393, 5431, 5443, 69499, 1019273
regulator: 4829231572580434769.12229618911003928172019249067341012087216528986395902
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:31:54 UTC
last updated: 2026-10-19 03:31:54 UTC

(-24048077303177977742, 61663015109312777595326062279)
(-23229331435044717056, 68809479756392843149666676575)
(5616172143607887730, 44003859221577253261691235271)
(9984367568076489778, 20143246656750511932732052039)
(11889519915381275170, 8170007228589006737797194679)
(12383054889836685274, 4414111760071332333554096335)
(14220338700035300850, 2893670168420032787456954439)
(14657071957759685314, 6834437490160689511283085271)
(36522937998687020338, 184009746631855111159969412743)
(39938442506380486258, 216816049331691834462683979463)
(50218420482872019766, 323143975666668511459025854123)
(-24220659416316966555422/1849, 7779798908444632334684408081148613/79507)
(-4798218151087383302606/225, 273091008989888600349065447425417/3375)
(-666428889092001655886/25, 1628769129113963669471925783227/125)
(69103577724018564343090/6241, 6666716291468355467646093489226441/493039)
(6888881855631556095136834/483025, 1129337213268654343518516628331727137/335702375)
(198438134873580623013333775/515524, 2790400290501047359544071880124303604723/370146232)

X400, T=1253/4597

last edited by Andrii Prokhorenkov at 2026-10-19 03:31:54 UTC · history