curve #5690

y² + xy + y = x³ − 2293700568413603163266103838x + 42140564195836232213537085590894836359188

a-invariants: [1, 0, 1, -2293700568413603163266103838, 42140564195836232213537085590894836359188]
c-invariants: [110097627283852951836772984201, -36409447465202669778936967729960893773814949]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 48209533267154336467449170843024227408211672914172713837973237716470
discriminant (Δ): 5149972147896675343984849657394750546325676100190407703523885719240874062012187500
Faltings height: 14.5373
naive height: 200.6135
primes of bad reduction: 2, 3, 5, 7, 31, 2221, 763666207, 37213484826946118843153, 117327405124968871201391495167
regulator: 52940770041608552036.644275369357407874988116115773540298250253710317181096828304
submitted by: apkorte
submitted at: 2026-10-24 10:41:45 UTC
last updated: 2026-10-24 10:41:45 UTC

Witness: 21 independent points log in to add more points →

(76815489690079, 564984744434476732985)
(17310158725804, -87310299339402145465)
(44341897174204, -166188885100094897065)
(29147582883454, 6927215690965122185)
(-13521757392521, -265862997014176169815)
(48036222540229, -206887463063813684065)
(66487412324179, -428428566159077381965)
(63655797482179, 392517956653272021785)
(122468720649751/4, -198365313819298932275/8)
(38115106227184, 100439393103298862315)
(9536837740664731/289, 239928375771563979450955/4913)
(6047822986324, 168789437798138701295)
(-15091697033336, -270775034907174222205)
(29276187234154, 9068318274912202085)
(-36766519502321, 277077294697599597785)
(-12869579659181, -263681597658807679495)
(32133716635804, 40198696256142676535)
(25446625583029, 15846036350368426835)
(5548407676819, 172002860947112368505)
(17633848452442, -84717700001901166315)
(18231360097552, 79894096178709965540)

Commentary

Specialization at T = 23/13 of the rank-17 fibration of X1008 given in curve#3589. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-24 10:41:45 UTC · history