curve #702

y² + xy + y = x³ − 1735685605337370863138x + 28910213719956459905992543396388

a-invariants: [1, 0, 1, -1735685605337370863138, 28910213719956459905992543396388]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 25397120877740310425144267566669140268544750140470
discriminant (Δ): -26414002311746365920518814946110389205518890509924780880593750000
Faltings height: 11.1253
naive height: 158.4066
primes of bad reduction: 2, 3, 5, 7, 11, 4593247033, 2393606210031683001241212553208206289
regulator: 193880698142335.110445516302551586823344815686788747542206706350867389639
submitted by: David Renshaw
submitted at: 2026-09-10 16:08:32 UTC
last updated: 2026-09-10 16:08:32 UTC

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

(22923691329, -1080840838684415)
(38161750704, 4271877833337460)
(45956268204, 6797273169599335)
(25021223304, 1070531318540260)
(35059016454, 3339299003356585)
(-11327111796, -6864192101700665)
(63121733829, 13070929239723085)
(-5656090671, -6208576948180415)
(4367494329, 4627408179012085)
(28388204229, -1585886238258515)
(20596327829, 1377888773000085)
(32021285604, -2482909909598465)
(1050208929, 5204664643325185)
(26261770689, 1200099415129345)
(93551345349, 26177848985864845)
(62648443704, -12886324289108540)
(33582914904, 2914781998294435)

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 16:08:32 UTC · history