curve #3981

y² + xy = x³ − 32031999994734161720x − 42299427644644228101925781184

a-invariants: [1, 0, 0, -32031999994734161720, -42299427644644228101925781184]
c-invariants: [1537535999747239762561, 36546705482666309080443015299135]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 2681265063185100898944986344566
discriminant (Δ): 1330497386457469064100801674266421983703188925211595834436352
Faltings height: 10.2370
naive height: 146.3534
primes of bad reduction: 2, 3, 7, 11, 19, 23, 61, 73, 127, 173, 457, 631, 3607, 1787719
regulator: 176779756449859.955142672897863074650790576624021511675349752
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:38:54 UTC
last updated: 2026-10-05 04:38:54 UTC

Witness: 11 independent points log in to add more points →

(-263324735074472/58081, 1381107152388335992744/13997521)
(-48997164843806/15625, -322774028118762620878/1953125)
(-197638453599944/58081, -2312655485905055696864/13997521)
(343058104186, -200905838536595294)
(4709367023331256/654481, 167241967052727067372832/529475129)
(130909691953864/11449, 1276828478117179556144/1225043)
(-10226969137981962/6661561, 981459751263936620127534/17193488941)
(-1863842489626604/990025, 104864913070403036061884/985074875)
(31260600487973736/4084441, -3310829733935214055661112/8254655261)
(897022694668881832/31281649, 832089671943545076248006896/174958262857)
(1412140645306984/2209, 53063953303454851132184/103823)

Commentary

Unlisted rational-isogeny neighbor of curve#3628 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 11: 11 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 04:38:54 UTC · history