curve #2858

y² + xy = x³ − 2353799432200918732090882185x + 39989567111692230080439457690563434811225

a-invariants: [1, 0, 0, -2353799432200918732090882185, 39989567111692230080439457690563434811225]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1131030138471108927870
discriminant (Δ): 143779644441407757176036169286451601583403885036517324174277610788190070724329000000
Faltings height: 14.6929
naive height: 200.6911
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 31, 59, 193, 199, 1847, 7307
regulator: 97859.1738749760072866481179157408145622958809657
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:37 UTC
last updated: 2026-09-26 20:25:37 UTC

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

(-13272789126870, -262474418962008447285)
(62997061649340, 376455986997155384865)
(235292735902330015/49284, 1858717131514493882047582075/10941048)
(26587804667725663180/471969, 95178457006708979892110235295/324242703)
(642213269652960633874197/709476496, 513932348728130104651370222396511867/18897615947456)

Commentary

Dujella - Lecacheux (2002). Source: https://dujella.github.io/tors/z2z6old5.html (curve entry 2). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:37 UTC · history