curve #466

y² + xy + y = x³ − 1556038331383338x + 23661751256860389864688

a-invariants: [1, 0, 1, -1556038331383338, 23661751256860389864688]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 3356653046043710479726709031837238710
discriminant (Δ): -743276271434381475440184156078589157200462500
Faltings height: 7.5027
naive height: 116.5594
primes of bad reduction: 2, 3, 5, 117361, 627391, 55161697, 27547709509171931
regulator: 111896382231.45554958303475921504495904692512709762018175692647818726
submitted by: Rayan Hatout
submitted at: 2026-08-31 09:26:29 UTC
last updated: 2026-08-31 09:26:29 UTC

(65904951377333/5726449, 1168966419192194129295/13703392457)
(1529754761/64, 5712161816265/512)
(154505371/9, -1210205446025/27)
(198608289285001/10810944, -1270006751919787296505/35546383872)
(27163829, -37924856565)
(11248126469/400, -370337317722993/8000)
(53530331/4, 578754814335/8)
(-13447861, 205323943215)
(-2161520141/81, 156672287505935/729)
(1670684309, 68267860032315)
(24311423, -14203608837)
(138781919, -1575096363195)
(1066343471/49, -3524775915795/343)
(53383154, -304534089540)
(88257128651/20164, 372605081341926225/2863288)

Mestre ten-root construction Roots 0,1,8,17,20,28,39,44,56,63

last edited by Rayan Hatout at 2026-08-31 09:26:29 UTC · history