curve #5537

y² = x³ + x² − 792006448360758674006206500x + 8524244644271856926999312020862335920000

a-invariants: [0, 1, 0, -792006448360758674006206500, 8524244644271856926999312020862335920000]
c-invariants: [38016309521316416352297912016, -7364947372651112482784533484523172022352064]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 91251885710022697113605305199452514975545635221752617836280
discriminant (Δ): 405227646305489906418561720824592803588715059015040591678426006621743077737120000
Faltings height: 14.2980
naive height: 197.4234
primes of bad reduction: 2, 3, 5, 7, 23, 67, 79, 177889249, 5016295709628117627296459763278349477800597
regulator: 228409919355434557.9254764055800931073184232077082793809789362694606878462915
submitted by: apkorte
submitted at: 2026-10-22 23:38:23 UTC
last updated: 2026-10-22 23:38:23 UTC

Witness: 19 independent points log in to add more points →

(-8563038077670, -121154182485084358470)
(-7190793230550, -117675746262117379350)
(5564268441390, -65494915351732179810)
(281727486946425/16, 393505249936470482475/64)
(100859587904370, -977063324625274358430)
(12674428383450, 22848417764694329850)
(7605290303010, 54228212441464968690)
(-1585967515026, -98875436636911191390)
(-17506035118662, 130476877897205727846)
(25516706194190, -70205660465810124990)
(-31891256315925, 36704930977689206400)
(11574652700640, 30128577998907850560)
(14969419513770, 4771591644514011030)
(34330649585572551/1849, -1178642746808670378923730/79507)
(17314126654224, 1325120947526534760)
(-3708962249082, 106821087292765321434)
(68764597395474, 528413136116941260990)
(-129664387374315/4, 92972156872466051145/8)
(14459907500130, -9762744235240526670)

Commentary

Specialization at T = -9/14 of the rank-17 fibration of X1008 given in curve#3594. 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 2026-10-22 23:38:23 UTC · history