curve #2857

y² + xy = x³ − 1644173544974177009215399260x + 29144075820496678960101949181880262179600

a-invariants: [1, 0, 0, -1644173544974177009215399260, 29144075820496678960101949181880262179600]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/7ℤ
conductor (N): 298298673786012728010
discriminant (Δ): -82469793783287598516267317999532844672521668550211278574722191517557792440320000000
Faltings height: 14.6370
naive height: 199.8693
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 31, 61, 83, 34483, 46199
regulator: 18019.9202265926705618855016333184143408715134324
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:33 UTC
last updated: 2026-09-26 20:25:33 UTC

(18840522713400, 69675800769119471460)
(-5279882261448, -194108035447655037084)
(28556991474360, 74025000283910777700)
(14185096013112, 93142882933735615332)
(-16480379716140, -227518256916697261800)

Elkies (2006). Source: https://dujella.github.io/tors/z7old5.html (curve entry 4). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:34 UTC · history