curve #4653

y² = x³ + x² − 91838015x + 744552964129

a-invariants: [0, 1, 0, -91838015, 744552964129]
c-invariants: [4408224736, -643320210355840]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 520723049109239936
discriminant (Δ): -189929575751217276702830848
Faltings height: 3.7311
naive height: 68.1953
primes of bad reduction: 2, 41, 71, 73, 79, 97, 617, 4049
regulator: 200048.571678413458083599937879975034442165849294420527
submitted by: The Wren
submitted at: 2026-10-20 17:36:03 UTC
last updated: 2026-10-20 17:36:03 UTC

Witness: 8 independent points log in to add more points →

(-4239, 1028446)
(-8288, 967711)
(282729/25, 134191958/125)
(5329, 637582)
(17896, 2198371)
(20055, 2639948)
(98185/16, 41085203/64)
(407239/9, -255054608/27)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Eight supplied rational points checked exactly on the displayed model. Rational torsion Z/2Z. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 17:36:03 UTC · history