curve #701

y² = x³ + x² − 61913406419306425121x + 179373218124120682171497955555

a-invariants: [0, 1, 0, -61913406419306425121, 179373218124120682171497955555]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 16036049986791945308616403080674328768139435391560
discriminant (Δ): 1289678401481255431088658033837742213129222628835533417811200
Faltings height: 10.2935
naive height: 148.3304
primes of bad reduction: 2, 5, 7, 19, 29, 24745331327, 4200437218901244361564317924591451
regulator: 401541860165921.716849018493013877949516752488907393206356051930448436644
submitted by: David Renshaw
submitted at: 2026-09-10 16:08:30 UTC
last updated: 2026-09-10 16:08:30 UTC

Witness: 17 independent points log in to add more points →

(6415555387, 214998664247290)
(5309275219, 17829613050074)
(3576362587, 60757108354810)
(3556345859, 64551969724326)
(-6669857093, 543695595938810)
(7757471807, 407325070491390)
(-307573599, 445406612471506)
(-389922753, 451060284489470)
(9791336782, 715441377149065)
(3290616647, -106166138663970)
(5647622830, 99218021151655)
(5735438607, 113760265569790)
(3085450239, 133101388342526)
(2073328257, 244783575193010)
(549565307, 381462630864390)
(-96518559, 430520744847214)
(2755271697, 172341718124030)

Commentary

Found by a search of rational specializations of Mestre families, using finite-field scores to select fibers and rational-point searches to construct the witness. Point independence checked with the site verifier.

last edited by David Renshaw at 2026-09-10 16:08:30 UTC · history