curve #2934

y² + xy + y = x³ + x² − 8007418165950294717261920x − 870716437481702091977368984017213055

a-invariants: [1, 1, 1, -8007418165950294717261920, -870716437481702091977368984017213055]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 548088118837830139058490
discriminant (Δ): 32531719420690972430975073726625714253395169331067396996901012701593600000000
Faltings height: 13.3710
naive height: 183.6408
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 47, 59, 61, 349, 21269
regulator: 61425.19430451141561932310202945296386394655112896947
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:29:01 UTC
last updated: 2026-09-26 20:29:01 UTC

Witness: 7 independent points log in to add more points →

(-383181597927, -1463323767915288287)
(3563438686053, 3980478568219330213)
(-137187778427, -474575037055755787)
(-691731404427, -2082612916549255787)
(-258315469397, -1086502037861948287)
(-1049448028427, -2525242524171255787)
(3335717042133, 3087935046864300853)

Commentary

Eroshkin (2008). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 67). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:29:02 UTC · history