curve #2943

y² = x³ + x² + 1374933729400516318549118185776672579795x + 81197013575416242358380437774253718563779553511837441125828

a-invariants: [0, 1, 0, 1374933729400516318549118185776672579795, 81197013575416242358380437774253718563779553511837441125828]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 4508790919021502851120376724936227453340
discriminant (Δ): -3014507510792456345676525711044093915272769411641743885472791321556086843554899158473519540437047416997093604660452750000
Faltings height: 21.7989
naive height: 284.8116
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 23, 37, 41, 47, 59, 67, 97, 113, 491, 577, 8287, 15325760017
regulator: 966487163.780496456761120676682277148844549710338387593
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:29:27 UTC
last updated: 2026-09-26 20:29:27 UTC

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

(13050589888772022503401/576, 4867548429454720644199199337831275/13824)
(1103154487921204503, -287602365034188870243708642057)
(-32967425917925634624, -6188879061380464310621855550)
(-177118811291355697132311/29584, -1372473530103474925375086970804276605/5088448)
(946565168977663762209/784, -6318928275680364661795653618121575/21952)
(-2961734911603264776072099/90601, -989791471799361771464151377057615175/27270901)
(619968963985707879833719776549/108904620049, -10734282571624695485538982560390199254749644275/35939286948510343)
(-32861552494431952299, -22977591285876174222339235275)

Commentary

2-isogenous image of D-z6old678-057, rational kernel x=65951374575037388855. 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 20:29:27 UTC · history