curve #4393

y² + xy = x³ − x² − 1036327194109x + 592685546138283889

a-invariants: [1, -1, 0, -1036327194109, 592685546138283889]
c-invariants: [49743705317241, -512080088016803352525]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 40259950941709401913212369600884639134
discriminant (Δ): -80519901883418803826424739201769278268
Faltings height: 5.9745
naive height: 95.3700
primes of bad reduction: 2, 366593, 54910965214433175092285408615119
regulator: 638196958955.50393022423112920738408960251427647529608802438527028696
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:21:33 UTC
last updated: 2026-10-17 10:21:33 UTC

(-306556, -938765627)
(-787889, -958823836)
(-667785, 993781957)
(435366, 473094685)
(737192, -479264745)
(-1180731, -411987772)
(691291, 454228785)
(781492, 509593653)
(832631, -554535996)
(-502992, -993072313)
(-1081656, 669957463)
(-1225557, -147671263)
(-803144, -951934921)
(1252991, 1122473949)
(1099288, -884789263)

BASE records/rank_15.md#13 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:21:33 UTC · history