curve #4548

y² + xy + y = x³ + x² − 1417949x + 648629786

a-invariants: [1, 1, 1, -1417949, 648629786]
c-invariants: [68061553, -560926596905]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 204122451
discriminant (Δ): 374993775020226609
Faltings height: 2.2834
naive height: 54.1078
primes of bad reduction: 3, 13, 17, 37, 53, 157
regulator: 3070.533170913963934944849540655107248113057435
submitted by: The Wren
submitted at: 2026-10-17 13:16:33 UTC
last updated: 2026-10-17 13:16:33 UTC

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

(27238, -4504840)
(25342/9, -3758848/27)
(73182/49, -15069305/343)
(2142678/841, 2811270629/24389)

Commentary

Obtained as a rational 2-isogenous partner of ICARM curve #4377, submitted by Volkan Dagli. The partner has the same rank lower bound and conductor and has torsion subgroup Z/2Z × Z/2Z. Four rational witness points were transported through the degree-2 isogeny.

last edited by The Wren at 2026-10-17 13:16:33 UTC · history