curve #5535

y² = x³ − x² − 25409835189929073308944x + 1559007898933612360793046254040064

a-invariants: [0, -1, 0, -25409835189929073308944, 1559007898933612360793046254040064]
c-invariants: [1219672089116595518829328, -1346982824671323047190492390377639360]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 132050268153089129424
discriminant (Δ): 12428166742473855400885255511833027945828799599831642104245981184
Faltings height: 11.4793
naive height: 166.3819
primes of bad reduction: 2, 3, 7, 17, 19, 149, 457, 631, 1481, 19121
regulator: 2787849.929897868795495056387597841785569068446777929
submitted by: Daniel Błażewicz
submitted at: 2026-10-22 23:26:03 UTC
last updated: 2026-10-22 23:26:03 UTC

(91823718570, 52694647430422)
(1111748822384/25, 2842139566308867552/125)
(1475772472225/16, 3010567713438537/64)
(83713289736960/961, 76299218907610336288/29791)
(491256170095576/5625, 1031702722893543821176/421875)
(1977470955885888/9409, 67697458214541095227840/912673)
(20864813157936280/1555009, 67743022542727148426068056/1939096223)

(u,v) = (19121,525623) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 7.

last edited by Daniel Błażewicz at 2026-10-22 23:26:03 UTC · history