curve #2809

y² + xy = x³ − 113302951502418682712521031916318985x + 21511951684944353479738305462052364088462449985347225

a-invariants: [1, 0, 0, -113302951502418682712521031916318985, 21511951684944353479738305462052364088462449985347225]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 207378196450271490213570
discriminant (Δ): -106823944732617416030358799767323582173740988672258596991452999865830259836585006945609995130535550668800000
Faltings height: 19.2377
naive height: 254.5240
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 29, 37, 83, 179, 421, 449, 5861
regulator: 230938.4247833852103331831290591961805227989981
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:23:25 UTC
last updated: 2026-09-26 20:23:25 UTC

Witness: 4 independent points log in to add more points →

(78814203761183644250/169, 581683965894328314177329774255/2197)
(3436332008458468416478730/34210801, 21124025259460851169358866870250108395/200098975049)
(1398754563943005473930/5329, 38620446628503258559292776320155/389017)
(11640543532109526978519663626/690060361, 1255666719143271256369948583563017883103663/18127195623109)

Commentary

2-isogenous to curve#1887 via the rational 2-torsion point x=203769462231968570. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny.

last edited by Natanael Wildner Fraga at 2026-09-26 20:23:25 UTC · history