curve #3960

y² + xy = x³ + x² − 2907011096793655995878676x + 1907729687644986825864441161381767680

a-invariants: [1, 1, 0, -2907011096793655995878676, 1907729687644986825864441161381767680]
c-invariants: [139536532646095487802176473, -1648278450126315141541722879592363599005]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 3682590235087728259825836306
discriminant (Δ): 9483634788704864364684565948484900056238531055313502227951058119048464
Faltings height: 12.6466
naive height: 180.6011
primes of bad reduction: 2, 3, 7, 11, 13, 17, 37, 53, 71, 131, 199, 311, 769, 1721, 3449
regulator: 1408409147350.5047319051739768801946006976775348703743630
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:34:46 UTC
last updated: 2026-10-05 04:34:46 UTC

Witness: 9 independent points log in to add more points →

(1282891082724, -538280721199788192)
(9274594093841388420/9406489, 38646989915929023227631840/28849701763)
(65709108225797076945/66455104, 3882301438885123083248314485/541742007808)
(48767500046833077156601/38865362449, -3719749216575499113144234750665714/7662034149283207)
(3491725482156010705/3538161, 23676102979768437298957405/6655280841)
(18582785464269145/18769, -24440907757968192049390/2571353)
(21733629214911145/12769, 1984029677932876325715650/1442897)
(541789291885967277976305/534289364401, 19981490413977838986465666439353510/390539345198275351)
(106828547283928418840505/65249082721, 20663080309929020237344192505669595/16667160441169519)

Commentary

Unlisted rational-isogeny neighbor of curve#3677 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 9: 9 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:34:46 UTC · history