curve #3088

y² = x³ + x² − 18930547595582330633859100826042865x + 743333575262731208284792941763359206829310485395775

a-invariants: [0, 1, 0, -18930547595582330633859100826042865, 743333575262731208284792941763359206829310485395775]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/4ℤ
conductor (N): 42724764594670256299980278974489087232160
discriminant (Δ): 195480334753275857554720411844528895724114934905184724618670791482668510842567973442811786548241600000000
Faltings height: 18.7206
naive height: 248.3919
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, 59, 67, 239, 409, 491, 880853, 37860733
regulator: 176826281.0053578433964442352332347883146230212465134565597
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:36:44 UTC
last updated: 2026-09-26 20:36:44 UTC

Witness: 10 independent points log in to add more points →

(20559514928248395, 19047862763645511972676500)
(39565101831733395, 7501975394540494976608500)
(28287947149303395, 15181023867991162550596500)
(-32685445410724035, 36430314859269554797617120)
(-11186576971152435, 30882061465346532434966280)
(118419368795569395, 12735866015645411612200500)
(124314225677221770, 17639517362720208634940625)
(182624320292371875, 58111756167727774877945580)
(110642430084334065, 1807888292870044459854780)
(23321632188969315, 17734906498764828289125780)

Commentary

Eroshkin (2008). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 30). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:36:44 UTC · history