curve #3594

y² = x³ + x² − 6139623020352439105319680x + 5864444230356397243663691375040002324

a-invariants: [0, 1, 0, -6139623020352439105319680, 5864444230356397243663691375040002324]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 359456687152396021072061767266447875854031596978527195696
discriminant (Δ): -45510765582629467215726988506361762522441934245073838290713850678375344128
Faltings height: 13.0265
naive height: 182.8471
primes of bad reduction: 2, 3, 7, 13, 19, 29, 37, 47, 1583, 9391, 63486094194947957461168473624954813101
regulator: 17475870025931274.45920567436668484932618501389639558499731773082965116827119
submitted by: wgxli
submitted at: 2026-09-29 06:48:58 UTC
last updated: 2026-09-29 06:48:58 UTC

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

(1430273129030, 94811848873283268)
(1445730045686, 99891227742074964)
(957449726774, 929390965222343148)
(980981206102, 886347176526496524)
(1091811180932, 680169460500328266)
(1185275345102, 502461212516830476)
(1198872153236, 476396305373384214)
(1217407238987, 440815279730791056)
(1260311571332, 358422394824438966)
(1321732545254, 241952312044507428)
(1496908710404, 167826757710805578)
(1509312031894, 189959390227993932)
(1596628329326, 363191798860054164)
(1699370975150, 581803612432683732)
(1854983584484, 926539923901149558)
(2210758918580, 1759602967473778518)
(2606653284524, 2751699456627725898)
(2614951928411, 2773192635515915964)
(-2264251387186, 2856160428770169612)

Commentary

Specialization at T = 8 of the rank-17 fibration of X1008 given by: y^2 + (Lx+B)y = x(x+D)(x+E), where B = pE + qD + pq(L-p-q), L = 46550T^2 + 1624T + 75424, p = -73708T^2 - 57738T + 135450, q = 71955T^2 + 77817T + 8760, D = 12(282127352T^4 + 191775362T^3 - 452929497T^2 + 78326358T + 840465), E = 153064275T^4 - 228008950T^3 + 1053019999T^2 + 5982765320T + 798799200.

last edited by wgxli at 2026-09-29 06:58:35 UTC · history