curve #711

y² + xy + y = x³ − 222469142523859833x + 34460003896785987245736268

a-invariants: [1, 0, 1, -222469142523859833, 34460003896785987245736268]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 5341166580058921769318328430443927865470
discriminant (Δ): 191679246420502364675854512058747300962839185791450000
Faltings height: 8.9468
naive height: 131.4443
primes of bad reduction: 2, 3, 5, 11, 61, 67, 73, 1039, 8677847, 82422216381668818301
regulator: 3315432195913.7948308614304494212161559685540057595197161604326757957
submitted by: David Renshaw
submitted at: 2026-09-10 16:08:45 UTC
last updated: 2026-09-10 16:08:45 UTC

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

(132614434, 2699863304915)
(116211839, 3189913503630)
(533295374, -8215469228685)
(80588867, 4129712414142)
(126198464, 2897277606780)
(121194014, 3045948574830)
(646875239, -12698102741070)
(408741314, -3437625734445)
(127109714, 2869729319130)
(496302839, -6804329216970)
(111837611/4, -42529541606925/8)
(1049929514, 30955491715155)
(354156659, -303263512410)
(111469619, 3323574270870)
(6251315309/16, -171527614743135/64)

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 16:08:45 UTC · history