curve #2805

y² + xy = x³ − 112990215345279616192969388342207278250x + 450679052475043122152258628678943621649365601242615639716

a-invariants: [1, 0, 0, -112990215345279616192969388342207278250, 450679052475043122152258628678943621649365601242615639716]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 6284587191562249335065454
discriminant (Δ): 4577206745132870014617559346625835314604136095834008860028712842956001441249814287515213966049398706773798018875392
Faltings height: 20.7795
naive height: 274.4747
primes of bad reduction: 2, 3, 7, 11, 19, 41, 61, 179, 337, 649849, 7302509
regulator: 723119.6269918372020379977887055386031757416926
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:23:14 UTC
last updated: 2026-09-26 20:23:14 UTC

(6696939383407955213350/961, 38890862058136309460245936458886/29791)
(-19899650118231499878584462/5583769, -375078398943804846695701003020808811092/13194446147)
(-783182741540466218088295340/96609241, -27421032732829902302805535229052268364114/949572229789)
(2392646277865369447057271336404/457967553289, 533825670332370617931227995532001114296175902/309921756239924837)

Dujella (2008). Source: https://dujella.github.io/tors/z10.html (curve entry 6). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:23:14 UTC · history