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curve #1280

y² = x³ − x² − 305210040x + 1705705257600

a-invariants: [0, -1, 0, -305210040, 1705705257600]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 48418471920
discriminant (Δ): 562878056378585619584640000
Faltings height: 3.8521
naive height: 70.2231
primes of bad reduction: 2, 3, 5, 7, 13, 29, 67, 163
regulator: 124.499343916234619280282409766347743169876355983
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:24:49 UTC
last updated: 2026-09-24 17:24:49 UTC

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

(110, 1293110)
(15190, 757770)
(646665, 519830220)
(56405/4, 3627715/8)
(-4240, 1709840)

Commentary

Torsion Z/2+Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:24:49 UTC · history

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