curve #5671

y² = x³ − 145020166x

a-invariants: [0, 0, 0, -145020166, 0]
c-invariants: [6960967968, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 1345974306986723584
discriminant (Δ): 195193417430949613947794944 ☆ record for quartic twists, rank ≥ 7
Faltings height: 3.7341 ☆ record for quartic twists, rank ≥ 7
naive height: 67.9908 ☆ record for quartic twists, rank ≥ 7
primes of bad reduction: 2, 17, 43, 281, 353
regulator: 167546.6524779694842429260543753528372438008766620532
submitted by: Michael Rubinstein
submitted at: 2026-10-24 04:20:51 UTC
last updated: 2026-10-24 04:20:51 UTC

(-12002, 108018)
(-9554, 716550)
(205411/9, 79083235/27)
(258043/9, 118957823/27)
(-5746, 802230)
(234073/16, 64303197/64)
(-4802, 765282)

Rank 7, proved: 7 independent points listed, matching the 2-descent upper bound. Torsion Z/2. Member of the family y^2 = x^3 + a x.

last edited by Michael Rubinstein at 2026-10-24 04:20:51 UTC · history