curve #4305

y² = x³ + x² − 571487662825x + 165611916360720039

a-invariants: [0, 1, 0, -571487662825, 165611916360720039]
c-invariants: [27431407815616, -143088860324109007360]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 7623567598977423232
discriminant (Δ): 96772201011560422077652346359980032
Faltings height: 5.5630
naive height: 92.8281
primes of bad reduction: 2, 17, 47, 89, 257, 769, 2801
regulator: 204809245.39118502379563956792896015500825025209114504527
submitted by: The Wren
submitted at: 2026-10-16 19:17:36 UTC
last updated: 2026-10-16 19:17:36 UTC

Witness: 9 independent points log in to add more points →

(1051954, -853542137)
(4126882, 8251832159)
(6533893/4, 15159092407/8)
(514042, 87598829)
(341436106/9, -6307809818239/27)
(81026026/169, -93828774911/2197)
(41187322/81, 58736402101/729)
(1998634, -2647081493)
(7622857/16, -2462829389/64)

Commentary

Obtained by a rational 2-isogeny from curve#4242, submitted by Michael Rubinstein and sourced from his elliptic-curves-by-rank repository. This isogenous curve has the same rank and conductor. The nine supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 19:17:36 UTC · history