curve #2851

y² + xy = x³ − 50693641981429217970733502331x + 4236624121693012204114505394297557612475345

a-invariants: [1, 0, 0, -50693641981429217970733502331, 4236624121693012204114505394297557612475345]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 927841267253365100790
discriminant (Δ): 583627380888072657234566331174654594226030906164220329542917447505832361905631620801600
Faltings height: 15.4148
naive height: 209.9004
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 73, 107, 181, 277, 1579, 2011
regulator: 211892.853509430046684063936127056005377715731783
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:18 UTC
last updated: 2026-09-26 20:25:18 UTC

(108696293830938, 103185468687769355481)
(193089718277808, 1283468049814857223911)
(53537120318946, 1294635771683411706549)
(151989120480858, 206871951370157723481)
(353299089897679681338/32137561, 349528215854277001002627687709749/182187833309)

Voznyy (2021). Source: https://dujella.github.io/tors/z2z6old5.html (curve entry 25). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:19 UTC · history