curve #2832

y² + xy = x³ − 801634269837107139166772851280x + 315710247481803582042676623278248394848262400

a-invariants: [1, 0, 0, -801634269837107139166772851280, 315710247481803582042676623278248394848262400]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/7ℤ
conductor (N): 20846457077884763415090
discriminant (Δ): -10089489280052470282128853476634369888806694555528023132829052088414611416865430405120000000
Faltings height: 16.1876
naive height: 218.4499
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 37, 43, 1350840962771
regulator: 15930.9011198473094061943555408856858658967184466
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:25 UTC
last updated: 2026-09-26 20:24:25 UTC

(85526630898592, 15740863331343335618992)
(290385834223569760/961, -299500046651904120799989680/29791)
(-178019446528040, -21278513390150019041480)
(-81372900992864, -19503915948192485780048)
(-437834763635540, -24140442806878317303980)

Elkies (2006). Source: https://dujella.github.io/tors/z7old5.html (curve entry 2). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:25 UTC · history