curve #2902

y² + xy + y = x³ + x² − 92612465495877847488461920x − 342308142750552501096807478081525053055

a-invariants: [1, 1, 1, -92612465495877847488461920, -342308142750552501096807478081525053055]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 548088118837830139058490
discriminant (Δ): 218441540503697394418566348625991914474920432200623399026711965906221415040000
Faltings height: 13.7176
naive height: 190.9850
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 47, 59, 61, 349, 21269
regulator: 1965606.217744365299818339264942494843646289636127023
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:37 UTC
last updated: 2026-09-26 20:27:37 UTC

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

(-5564460649447, 858283024373587233)
(28417212774053, -141329000524103357787)
(-464983321725995/81, 295986921239440592621/729)
(-5425744871467, 675688434102402453)
(-50810162552573/9, 20980234717329380251/27)
(-48175093165955/9, 6437956080208839223/27)
(25430074808813, -117251418131252685387)

Commentary

2-isogenous image of D-z2z4old678-067, rational kernel x=2882616151573. Source: https://dujella.github.io/tors/z2z4old678.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 20:27:37 UTC · history