curve #703

y² + xy + y = x³ − x² − 368788289807005911653x + 2696456309772386395301917825437

a-invariants: [1, -1, 1, -368788289807005911653, 2696456309772386395301917825437]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 279994905038222043921553771939795968394925362682730
discriminant (Δ): 69027925774446116816158334429346363019479418180162153140633600
Faltings height: 10.6756
naive height: 153.6839
primes of bad reduction: 2, 3, 5, 17, 31, 47, 5857193, 87980865933329, 243736953959434452071729
regulator: 2654814037986661.73730441074411945057267427212064853070382580110692603856
submitted by: David Renshaw
submitted at: 2026-09-10 16:08:34 UTC
last updated: 2026-09-10 16:08:34 UTC

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

(12876334463, -287601742362912)
(18487999103, 1482424501177248)
(-3603034897, 1994604341184048)
(251725782983, 125939090149009728)
(585040163, 1575087194400288)
(-13960941889, -2263616298545376)
(12107548733, -78827482246962)
(14442670535, 618681524589816)
(45816232313, 9053929996705938)
(10032881225, -79654493472204)
(-8631613965, 2288365768543148)
(12052780527, 49325653250352)
(-15988844505, 2122628162694168)
(25476103175, -3136247698855872)
(-20243287897, 1366184567552448)
(75231276575, 20018500843586496)
(1741623293, 1435077111690228)

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 16:08:34 UTC · history