curve #2930

y² + xy + y = x³ + x² − 99693354254976736309048235x + 367381667413491416441937241575243024665

a-invariants: [1, 1, 1, -99693354254976736309048235, 367381667413491416441937241575243024665]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 23959330209511704615223770
discriminant (Δ): 5106310644853957469804174516316205640090151672922763521755210984300846120960000
Faltings height: 13.8638
naive height: 191.2060
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 23, 31, 41, 43, 97, 193, 241, 2087, 2713
regulator: 442159.1380330481429920975426283075068146906381826735
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:50 UTC
last updated: 2026-09-26 20:28:50 UTC

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

(-835742939437, -21215935717377581002)
(3746954832963, 6814774952116046038)
(-6096171578085, -27360105846461167706)
(-2303622473757, -24182904784189102202)
(2494935489403, 11583755159287549598)
(1441480579203, 15055590839860301398)
(7012677573523, 3623709821741193398)

Commentary

Dujella (2005). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 54). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:51 UTC · history