curve #2946

y² + xy = x³ − 342517264406531145321584963405169346145200x + 149546165808168350076798749197633417815774001516503322573183232

a-invariants: [1, 0, 0, -342517264406531145321584963405169346145200, 149546165808168350076798749197633417815774001516503322573183232]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 220989850677256034459433715825098922710
discriminant (Δ): -7089530203447088933947656724816219616634747166497758236612542854135787590504504040311532788195124822601318359375000000000000000
Faltings height: 23.0315
naive height: 299.8486
primes of bad reduction: 2, 3, 5, 11, 13, 17, 23, 41, 73, 79, 109, 163, 911, 1609, 22651, 428083, 2206483
regulator: 1692043771.69176290219930430312909693718418370472719238
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:29:35 UTC
last updated: 2026-09-26 20:29:35 UTC

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

(65648499187634578321978696/85849, 460245050804961810135240187555909683536/25153757)
(149720261173924935535483649504/243391201, 49743963291846902957520308683001218512404048/3797146126801)
(630319842134658324704, 13567563052296719979832552397648)
(-2053365270938642401853536/73441, -251040716467915501848891376861136345872/19902511)
(574924369459930197004, -11943994824662679066680727739052)
(194299636158527022299175296/196249, 2429496924351087763674547200197451421936/86938307)
(-80562075463080071840551353056/111957561, -5733292040643182024031457607327275254157232/1184622952941)
(110521636242992421156276232336/87179569, -34079321364608354746789273823529575013045296/813995635753)

Commentary

2-isogenous image of D-z6old678-080, rational kernel x=369145749764614618976. 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 20:29:35 UTC · history