curve #3378

y² = x³ − 260211x − 20063630

a-invariants: [0, 0, 0, -260211, -20063630]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 27127152
discriminant (Δ): 953703558817910784
Faltings height: 2.1432
naive height: 49.0213
primes of bad reduction: 2, 3, 13, 43, 337
regulator: 43.24318052489523385678178765307101708180803617
submitted by: David Renshaw
submitted at: 2026-09-26 21:17:23 UTC
last updated: 2026-09-26 21:17:23 UTC

Witness: 4 independent points log in to add more points →

(-430, 3510)
(-423, 3784)
(-391, 4680)
(-337, 5418)

Commentary

Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = -387, b = -1011; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 27127152, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-26 21:17:23 UTC · history