curve #3034

y² + xy = x³ − 2381920949644307887460933092015x + 1156062937771153323922678483670947135438823225

a-invariants: [1, 0, 0, -2381920949644307887460933092015, 1156062937771153323922678483670947135438823225]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 11357092358577020158149155010
discriminant (Δ): 287532236923454894119706249750797472867754200513402198488875730518568634681202936000000000000
Faltings height: 16.4584
naive height: 221.4500
primes of bad reduction: 2, 3, 5, 11, 37, 43, 47, 101, 149, 223, 283, 359, 379, 3561661
regulator: 5709888.93715248526944950572619785934728704207566214218
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:34:14 UTC
last updated: 2026-09-26 20:34:14 UTC

Witness: 8 independent points log in to add more points →

(1272371267164730, 13610783611195456007585)
(143283255221570, 28595719341002078612885)
(10746842713203670/9, 102586397844975735784495/27)
(-731465657716954, 50069866125867420306557)
(683781524782652035670/11449, -17874428724753204796938835129145/1225043)
(2250371866687430, -84806420120493053778115)
(10508811325050280882070/17689, -1077280821199456157467010362617655/2352637)
(5464689736590103670/4489, -2338902792360839738927875345/300763)

Commentary

2-isogenous image of D-z6old678-052, rational kernel x=-593182814314362. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:34:14 UTC · history