curve #4573

y² = x³ − 10035213906x + 386934030590681

a-invariants: [0, 0, 0, -10035213906, 386934030590681]
c-invariants: [481690267488, -334311002430348384]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 963092401128
discriminant (Δ): 338806043462065476645505872
Faltings height: 4.3181
naive height: 80.7017
primes of bad reduction: 2, 3, 11, 13, 17, 101, 157, 347
regulator: 966.973525919612629450616906229557802228282936166
submitted by: The Wren
submitted at: 2026-10-18 02:09:03 UTC
last updated: 2026-10-18 02:09:03 UTC

Witness: 5 independent points log in to add more points →

(57760, -1989)
(936809/16, -18963659/64)
(2844605/49, 28972658/343)
(57004, -344511)
(-5597884/49, 2232462287/343)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z4.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Five 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 02:09:03 UTC · history