curve #3057

y² + xy = x³ − 23240401552546314845230555767250x + 39035737383640548738264240132679708432408668932

a-invariants: [1, 0, 0, -23240401552546314845230555767250, 39035737383640548738264240132679708432408668932]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 27945024266811292803708345030
discriminant (Δ): 145084448935738519618593364955279020010298843831556341576434203817845451452471505554180669440000
Faltings height: 16.9948
naive height: 228.2839
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23, 41, 47, 83, 103, 107, 149, 157, 353, 389, 4889
regulator: 2603435.11138096018842283363770839856804105194145195670
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:35:17 UTC
last updated: 2026-09-26 20:35:17 UTC

Witness: 8 independent points log in to add more points →

(2040837862129604, 10294405331164056123998)
(1546125919559684, 82457093881535497643678)
(1127689628153444, 119422955102773909527518)
(1146935474467964, 117852641604632336320958)
(1559355735815744, 81162787604838366316418)
(-2633076962819836, -286311249696516774300322)
(-2051742007175356, -279431456561050060030882)
(3795308235097924, 74163692520455985675358)

Commentary

Dujella - Peral (2012). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 7). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:35:17 UTC · history