curve #4566

y² = x³ − x² − 5042999x + 4351881408

a-invariants: [0, -1, 0, -5042999, 4351881408]
c-invariants: [242063968, -3758573152736]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 1360863192
discriminant (Δ): 32903641419539132112
Faltings height: 2.6257
naive height: 57.9141
primes of bad reduction: 2, 3, 13, 17, 47, 53, 103
regulator: 173.6797048667416339087574321892813240470044028
submitted by: The Wren
submitted at: 2026-10-18 02:03:29 UTC
last updated: 2026-10-18 02:03:29 UTC

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

(1357, 2353)
(9652/9, 358046/27)
(31156/25, 130754/125)
(592, 39668)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z4.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Four supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C4. Source-attributed existing curve.

last edited by The Wren at 2026-10-18 02:03:29 UTC · history