curve #2881

y² = x³ − x² − 84385099279492765124x + 262973362131816463305769975044

a-invariants: [0, -1, 0, -84385099279492765124, 262973362131816463305769975044]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 407883563785258865304
discriminant (Δ): 8582210155966085867798931946696261757455247241309002279487744
Faltings height: 10.4207
naive height: 149.2594
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 29, 31, 383, 1999, 76369
regulator: 47739.661534024435690336117489393110976533991719468
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:40 UTC
last updated: 2026-09-26 20:26:40 UTC

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

(12885805880, 1146827806213782)
(7979506940, 312565640755122)
(604008660, 460678184564598)
(1473384440, 376616759777622)
(15209138914, 1580409705748016)
(20163601480277, 90542423098869511770)

Commentary

Dujella (2001). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 70). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:26:40 UTC · history