curve #2844

y² + xy = x³ − 19743860929325035502863459210x + 4096735464261663217563807627752085945979172

a-invariants: [1, 0, 0, -19743860929325035502863459210, 4096735464261663217563807627752085945979172]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/8ℤ
conductor (N): 4120457237924781091170
discriminant (Δ): -6757780936890336538798111447653495718994599217794469895310976364713474055860412900000000
Faltings height: 15.5358
naive height: 209.7607
primes of bad reduction: 2, 3, 5, 7, 17, 29, 41, 43, 61, 79, 157, 29838041
regulator: 74189.6912756109100674779144398062871644060780257
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:59 UTC
last updated: 2026-09-26 20:24:59 UTC

Witness: 5 independent points log in to add more points →

(64786343948084, 1757705489176705699958)
(23596343445404, 1908923949002165628518)
(-36402206521336, -2183396018286616851502)
(161860995539084, 2267502458684815282958)
(7071203454338, 1989340636071804829946)

Commentary

Dujella - Peral (2012). Source: https://dujella.github.io/tors/z8old5.html (curve entry 10). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:00 UTC · history