curve #708

y² = x³ − x² − 1116967888345036739440x + 16973991578891101450370139259600

a-invariants: [0, -1, 0, -1116967888345036739440, 16973991578891101450370139259600]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 1515730060005137101916372394537870946564523760
discriminant (Δ): -35279181622214918383704381053293748397929855527312697087664000000
Faltings height: 11.1053
naive height: 157.3416
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 79, 149, 17520038214541, 190021288921368841319
regulator: 2678041266384.363402120755994727589387092320860488218805851537009150199
submitted by: David Renshaw
submitted at: 2026-09-10 16:08:41 UTC
last updated: 2026-09-10 16:08:41 UTC

Witness: 16 independent points log in to add more points →

(191704872840, 82753521046416220)
(-28016615300, 5126065628570040)
(32458350405, 3862042642508050)
(-34844374370, -3686247925395750)
(-8110362780, -5049705243903320)
(16743771525, 1722184034881310)
(46299152380, -8031607629045000)
(-33101334170, -4204526434727850)
(-2492590620, -4443270054223000)
(144129652420/9, 48249900187775000/27)
(44035911400, 7292464350110940)
(-206323622180/9, 149191035647053400/27)
(7562173880, 2993282520442500)
(29706367630, 3163520181243750)
(21666625630, 1715897725395750)
(26195643812, -2385384105770952)

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 16:08:42 UTC · history