curve #2887

y² + xy = x³ − 6830221225005750458928866x + 7951738746006835065576060128812352580

a-invariants: [1, 0, 0, -6830221225005750458928866, 7951738746006835065576060128812352580]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 1310089338214953805719210
discriminant (Δ): -6922275751026239675846050387723954694055305498717215741367332020102555402240
Faltings height: 13.2756
naive height: 183.4561
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 131, 397, 887, 5527, 5900281
regulator: 18348579.86860863238398632084634948259601657499946941
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:55 UTC
last updated: 2026-09-26 20:26:55 UTC

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

(1678322292964, 1102662708145815886)
(-309003411998467604/3728761, -21013337255711218876520227990/7200237491)
(219065180327962420/124609, 51625598263637254620971390/43986977)
(-1568919454865180/9409, -2751072362238009729942770/912673)
(21675497412008836/10201, 1794069310226596935820310/1030301)
(127289886854656/529, 30592584718031968464062/12167)
(98645308763091499/100, -30982263217926012007562213/1000)

Commentary

2-isogenous image of D-z6old678-132, rational kernel x=1534675231588. 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 20:26:55 UTC · history