curve #2927

y² + xy = x³ − 150896123934128959243712285x + 844403124386456716996509171987377289009

a-invariants: [1, 0, 0, -150896123934128959243712285, 844403124386456716996509171987377289009]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/5ℤ
conductor (N): 66962884494658686917988066
discriminant (Δ): -88128758007951727700623417517995188168956420423430962364900089911158511036563456
Faltings height: 14.0595
naive height: 192.7865
primes of bad reduction: 2, 3, 7, 11, 17, 19, 41, 67, 937, 2729, 63883377511
regulator: 1901912.265124174075667012772353512424460983016866205
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:43 UTC
last updated: 2026-09-26 20:28:43 UTC

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

(6185569421986, 12152873534380947055)
(7399018466710, 11531808471208398823)
(6877371129730, 11485726171880266063)
(5996702988790, 12456642032009666983)
(3438036957610, 19137777873360242623)
(-14425657901400, -4382373755072136297)
(-13501730569340, -20504642078577659777)

Commentary

Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 20). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:28:44 UTC · history