curve #235

y² = x³ − 6073700298618828x + 175770017627867226340148

a-invariants: [0, 0, 0, -6073700298618828, 175770017627867226340148]
c-invariants: [291537614333703744, -151865295230477283557887872]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 690285168700675717325304943706298441927480
discriminant (Δ): 993016632286044059915490679818132686619195628800
Faltings height: 7.9761
naive height: 120.6418
primes of bad reduction: 2, 3, 5, 37, 61, 1061, 11174227, 71657492841305578040354317
regulator: 1930058946037.1760717909398678090108062436141414502209083178458576916
submitted by: RoyManami
submitted at: 2026-06-26 01:21:19 UTC
last updated: 2026-07-01 22:41:38 UTC

Witness: 15 independent points log in to add more points →

(33929674, 93551911110)
(55028554, 90428617530)
(51848404, 15497923230)
(51767374, 8936997390)
(20389894, 245774216430)
(34564594, 84437781030)
(53046094, 53382700530)
(26873404, -178763660730)
(-29739926, 574541160390)
(65790004, 246863819070)
(-36266726, 590205480390)
(-6254546, 462075298830)
(70278844, 309891494970)
(31681258, 123069479994)
(57653926, 131291923986)

Commentary

Rank-15 naive-height record: h=120.642 (beats 127.132). New 3-parameter sub-family of Mestre locus 12*p5=5*p2*p3: six roots = union of two depth-2 cubics with (p-r)(q-s)=0 (equal product), beyond Mestre (u,v) slice. Sextuple {0,7,133,136,430,434}, T=162; base-point injection + Neron-Tate independence (15 indep).

last edited by RoyManami at 2026-06-26 01:21:19 UTC · history