curve #3067

y² = x³ − x² − 16275673326928004830300499825x + 22374180470634970227928749712599947693981025

a-invariants: [0, -1, 0, -16275673326928004830300499825, 22374180470634970227928749712599947693981025]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/4ℤ
conductor (N): 261177474612557023438148127247354080
discriminant (Δ): -215984978453246842484728532096134101898034315817364583602411449945111822862813681713254400
Faltings height: 15.8208
naive height: 213.1561
primes of bad reduction: 2, 3, 5, 7, 11, 17, 41, 71, 139, 157, 211, 229, 283, 3547, 5651, 3410431
regulator: 1578920993.8898403897227873265929180851503555154049438270
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:35:43 UTC
last updated: 2026-09-26 20:35:43 UTC

Witness: 9 independent points log in to add more points →

(-77014662931824, 4813611129563743070025)
(-106173766036725, 4785953101507739912520)
(31413536475375, 4679092135601877391020)
(96000948900701, 4657946180745108640620)
(540550068665225925, 397423806070678002049531020)
(230752447751901, 5559256565264735519340)
(-79459122953443, 4813080716618069800212)
(-65863763757800, 4812529297203127196605)
(11734315925224435105/2704, 40184485126455200520458751625/140608)

Commentary

Dujella (2009). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 46). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:35:43 UTC · history