curve #2841

y² + xy = x³ − 36180559909936665984616479270x + 2653605664924418914307133525288436083708900

a-invariants: [1, 0, 0, -36180559909936665984616479270, 2653605664924418914307133525288436083708900]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/7ℤ
conductor (N): 887644055522613612630
discriminant (Δ): -10842342311707233347442439474925484506204284929600955722084264520855441137500160000000
Faltings height: 15.2027
naive height: 208.8921
primes of bad reduction: 2, 3, 5, 11, 29, 31, 59, 151, 337609, 994769
regulator: 61550.5955432289476463936806509220441089963984636
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:52 UTC
last updated: 2026-09-26 20:24:52 UTC

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

(47596634272620, 1019490087452772331530)
(65357521331220, 753734338701716054250)
(37071254323980, 1167601425603747441930)
(110821323250140, 71171122159540704330)
(20835879745863744/169, 568498652465192600946354/2197)

Commentary

Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z7old5.html (curve entry 9). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:52 UTC · history