curve #2994

y² = x³ − 92885921348572977494474885609821287x + 11073454318107101891244347067880697710513194186209566

a-invariants: [0, 0, 0, -92885921348572977494474885609821287, 11073454318107101891244347067880697710513194186209566]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 1983849109508312439665107289994540
discriminant (Δ): -1682800350522981713867877293265382978405815698001043249285206397817147687986571564214790330266643801248000
Faltings height: 18.9854
naive height: 253.1959
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 47, 83, 97, 103, 127, 307, 10333, 94388321
regulator: 320212426.367160890996217503649355500577904420251979357
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:32:25 UTC
last updated: 2026-09-26 20:32:25 UTC

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

(-10370628239950029, 109706993016836356703511950)
(95989558252153515, 55152725208899482417559306)
(-246659864769360093, 137759313149344684718350430)
(29626406927519858133243/146689, 1319911513211841445985081132240870/56181887)
(18801534939676913906639313327443627/17469458995870561, -2484424899604889031649327944923832078873263709053430/2308974749428382454007441)
(7777619172105062883/49, 6221091740689884108397039330/343)
(133780549011938434383363/779689, 9423232677077201783081107441945330/688465387)
(18865350498723186137/16, -79441595761507746065665432605/64)

Commentary

2-isogenous image of D-z6old678-091, rational kernel x=176277529846152827. 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 20:32:25 UTC · history