curve #6452

y² + xy + y = x³ − x² − 659888245878635139019633587x + 6553304237791888700441475216764044222995

a-invariants: [1, -1, 1, -659888245878635139019633587, 6553304237791888700441475216764044222995]
c-invariants: [31674635802174486672942412161, -5662054861452049301320324802094105967813185]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 2650924714524729280604679360158389934142442401281957350228960917518
discriminant (Δ): -162185054857964729892399113750292129073415396701482021842906148602370461928194048
Faltings height: 14.2374
naive height: 196.8847
primes of bad reduction: 2, 13, 17, 23, 31, 41, 31645511, 6483203073927472081216855363355004437893279885416133
regulator: 23298120001540348676.320925644817709023197512868885726652004040391652533854192265
submitted by: apkorte
submitted at: 2026-11-03 16:55:02 UTC
last updated: 2026-11-03 16:55:02 UTC

(12742673422443, 14617266725164419314)
(4380994444037, -61208027949740434180)
(30268636370491, -119629523867292442974)
(30019341932965, 117456999439832535294)
(17556724931385, 19480442008714683150)
(153738515521267/9, 439978037936568153878/27)
(15542754216763, -7183224312345003486)
(18840312012603, -28430822704213617118)
(9323614055771, 34803165067366260386)
(16045174811643, 9801740837009385314)
(103964722805947, -1030372761012189346910)
(48906154862700331/3025, 1749157363723885102151214/166375)
(-26144426483237, 77040113318856996514)
(25545218367177, -79787581608378923250)
(-7766712546919, -105877114942981285544)
(14597792980267, 5578263284472240802)
(21100269975663, -44986405028845958178)
(16688998571671, 13736612133752261686)
(35865985376315, 170360336811347871394)
(17996347997267, -22498380031498775198)
(35520354445371, -167121871660060872414)

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