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curve #2639

y2 + xy = x3 − 12163174x + 1409363924
a-invariants
[1, 0, 0, -12163174, 1409363924]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
253506
discriminant (Δ)
114305739964226647136784
Faltings height
3.1141
naive height
60.5554
primes of bad reduction
2, 3, 11, 23, 167
regulator
30.8553159876079266358067789058809713768294
submitted by
Natanael Wildner Fraga
submitted at
last updated

Witness: 2 independent points log in to add more points →

Commentary

2-isogenous to curve#2069 via the rational 2-torsion point x=1772. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at · history

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