curve #3141

y² = x³ − 6471600729124446568604333138291652x − 917122040913371619991977065053051586271999234304

a-invariants: [0, 0, 0, -6471600729124446568604333138291652, -917122040913371619991977065053051586271999234304]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1960485463586913342377444285725055962941120
discriminant (Δ): 17346266823216634448421831733391117343567737968987290754188809870298637371239672701694683578753600000000
Faltings height: 18.4992
naive height: 245.1718
primes of bad reduction: 2, 3, 5, 7, 23, 29, 37, 59, 79, 83, 107, 241, 293, 317, 397, 421, 1933, 3067, 4291829
regulator: 25303286856.0357657271055495319119518578603422740002856318025
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:39:13 UTC
last updated: 2026-09-26 20:39:13 UTC

Witness: 11 independent points log in to add more points →

(-12793660406913038, 8932205912895850161472560)
(189574190785056362, 74734346455668439058889160)
(-21158691994093838, 11249041934869266241178640)
(633406205880926122, 500024667298475430178425000)
(-19509817281953428, 10858938530195004680340700)
(-31804645144040603, 13142994960732677323962525)
(2445339151125378922, 3821848787524139938190896200)
(1407641774730283622, 1667353812254388502362965000)
(-70444197244197338, 10266371010350440733177640)
(90876608801761522, 12707300944402098128211600)
(2230001413660476202, 3327935620485059992848683880)

Commentary

Voznyy (2023). Source: https://dujella.github.io/tors/z2z2old1011121314.html (curve entry 58). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:39:13 UTC · history