curve #3107

y² = x³ + 4692726937524378378756566939402025

a-invariants: [0, 0, 0, 0, 4692726937524378378756566939402025]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 506814509252632864905709229455418700
discriminant (Δ): -9513368399592114216026817528774039320639147456334884463176696011470000
Faltings height: 12.1065
naive height: 168.5858
primes of bad reduction: 2, 3, 5, 7, 23, 31, 37, 43, 83, 109, 151, 421
regulator: 649906989.0556765515763338446278463824745495937534048129731
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:37:36 UTC
last updated: 2026-09-26 20:37:36 UTC

Witness: 10 independent points log in to add more points →

(-135797482140, 46781315964225555)
(-150436201545, 35891470127810220)
(-42200591214, 67952721291406041)
(2327642247924, 3551854243978575507)
(5504535148140, 12914782107290941395)
(140506152430, 86409469562070095)
(397507563420, 259814927561209005)
(7162660587075, 19169656506442936830)
(73148794740, 71303068454026605)
(-102758626586, 60063833881519937)

Commentary

Elkies - Rogers (2004). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 46). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:37:36 UTC · history