curve #88

y² = x³ − 932733487x + 11052354147250

a-invariants: [0, 0, 0, -932733487, 11052354147250]
rank (lower bound): ≥ 12
conductor (N): 26145292874820119408329144
naive height: 73.5905
Faltings height: 3.9878
discriminant (Δ): -836649371994243821066532608
primes of bad reduction: 2, 125207, 26102067850459758049
regulator: 58563136.762357434222764319524246397648310277411773547153070685
submitted by: David Renshaw
last updated: 2026-07-01 22:46:37

Witness: 12 independent points

(361, 3273482)
(877, 3199222)
(1425, 3118670)
(-1927, 3583654)
(2026, 3028358)
(-2363, 3639122)
(3001, 2877542)
(-3261, 3749576)
(3533, 2793046)
(-4019, 3838762)
(-4394, 3881488)
(4394, 2653066)

Commentary

Smallest known conductor (N = 26145292874820119408329144) elliptic curve of rank >= 12, announced by Noam D. Elkies in 'New elliptic curves of large rank and low conductor' (preliminary report, JMM Special Session on arithmetic geometry informed by computation, Boston, January 4, 2023). Witness points found by ellratpoints and certified independent by Neron-Tate height pairing.

last edited by David Renshaw at 2026-06-11 16:54:49 · history