curve #3074

y² + xy + y = x³ − x² − 176620653974058428143264127x + 903414674763811890417046406006315779751

a-invariants: [1, -1, 1, -176620653974058428143264127, 903414674763811890417046406006315779751]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/4ℤ
conductor (N): 110072036541366600851273211270
discriminant (Δ): 37680625595733672595162394125080255054776863668468923554151621660697600000000
Faltings height: 13.7532
naive height: 192.9217
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 37, 41, 59, 67, 257, 3203, 48539, 173659
regulator: 41591232.551277112363905114446882573145299362399599645153
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:36:02 UTC
last updated: 2026-09-26 20:36:02 UTC

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

(7768993064691, 406346675232305014)
(4347401613651, 14755987046504074774)
(8207792508501, 2586575356972455874)
(7770133855251, 412584154102196374)
(15728276331, 30010610452491148414)
(249263407251, 29315611689872948374)
(4777788280851, 12985466545844741974)
(7865802003931, 902972932760584854)
(7764585247251, 382035197041964374)

Commentary

Eroshkin (2008). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 42). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:36:02 UTC · history