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curve #2489

y2 + xy + y = x3 − 911242494x + 7481345356576
a-invariants
[1, 0, 1, -911242494, 7481345356576]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
3148530
discriminant (Δ)
24246605265337839660888704400
Faltings height
4.1527
naive height
73.5046
primes of bad reduction
2, 3, 5, 7, 11, 29, 47
regulator
6.687638874724391497235886832640977569413
submitted by
Natanael Wildner Fraga
submitted at
last updated

Witness: 1 independent point log in to add more points →

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-20, q=9; A=(3q-p)(p+q)^3=-62557, B=-(p+3q)(p-q)^3=170723. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at · history

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