curve #2883

y² + xy = x³ − 13050070927054823465x + 16542549296816918233072779225

a-invariants: [1, 0, 0, -13050070927054823465, 16542549296816918233072779225]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 4947820003357601370
discriminant (Δ): 24019602288923190802517294890354398020163184647979829760000
Faltings height: 9.9392
naive height: 143.6596
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 31, 41, 43, 61, 109, 149, 179
regulator: 2721.3567124122026437071973490288924659446715631707
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:44 UTC
last updated: 2026-09-26 20:26:44 UTC

Witness: 6 independent points log in to add more points →

(1096220890, 59615874435235)
(899520022, 74374166104447)
(392536090, 107146475356675)
(435448162, 104606127424147)
(686748970, 88905865222435)
(896843530, 74565188888035)

Commentary

Eroshkin (2008). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 103). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:26:44 UTC · history