curve #2913

y² + xy + y = x³ − 2449048185109017307868x + 43684440977362864278827303019056

a-invariants: [1, 0, 1, -2449048185109017307868, 43684440977362864278827303019056]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 4439405348342065911810
discriminant (Δ): 115696752797146325107688309040926887790253470009441841354155531250
Faltings height: 11.2315
naive height: 159.3636
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 29, 79, 257, 523, 631, 1741
regulator: 69568.28038509566686978346242242977943687837179729251
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:06 UTC
last updated: 2026-09-26 20:28:06 UTC

Witness: 7 independent points log in to add more points →

(-109727782502760/2209, 679009964953423774361/103823)
(-3747231430834041/592900, -3504031222547641336325167/456533000)
(1581136020630990/10609, -59742521762738899451936/1092727)
(5593803960241466460/177241, -13230015961731509654800338848/74618461)
(1262121443071260, -44838566927104430161568)
(141754883355/4, -9468909878808469/8)
(52357694878260, -378852897294737672693)

Commentary

2-isogenous to curve#1265 via the rational 2-torsion point x=28368135073. Independent witness points are the images of that curve's witnesses under 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 20:28:07 UTC · history