curve #3990

y² + xy + y = x³ + x² − 120173294149979442510360x + 16033036983896224913722494070540761

a-invariants: [1, 1, 1, -120173294149979442510360, 16033036983896224913722494070540761]
c-invariants: [5768318119199013240497281, -13852543954129600711350227476250947265]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ
conductor (N): 3070143408623089579456273867631802
discriminant (Δ): 22641140849527113851944380619876375069395668097762309633319687759872
Faltings height: 11.9498
naive height: 171.0433
primes of bad reduction: 2, 3, 11, 17, 19, 29, 59, 67, 97, 149, 151, 307, 349, 353, 2083, 2297, 3181
regulator: 208323921825272.96641126598785113420826111087044256466932750642
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:40:45 UTC
last updated: 2026-10-05 04:40:45 UTC

Witness: 12 independent points log in to add more points →

(120756727232101/81, -1293911795053632456091/729)
(2916291742506811/12321, -39855221058234255971929/1367631)
(212566867441, -9640683071029183)
(9887804979229/49, -432038526700549/343)
(126912084027499/625, 29198104316744122643/15625)
(216196280501, 12538302278503101)
(7284632734456829/24649, 307890010445894550423153/3869893)
(26277699323489, 134692484491904967249)
(165053195711227861/106929, -65492650714870972407845093/34965783)
(657697413460861/3249, 228026673956497509373/185193)
(5393212460509/25, 1520548192246297513/125)
(7397013230621171/34225, 79046985939160684432401/6331625)

Commentary

Unlisted rational-isogeny neighbor of curve#3631 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 12: 12 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:40:46 UTC · history