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curve #2251

y2 + xy = x3 − 13378918677576x + 18785382249971926080
a-invariants
[1, 0, 0, -13378918677576, 18785382249971926080]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
4865910
discriminant (Δ)
816257889320087343675853262678497689600
Faltings height
6.3345
naive height
102.2877
primes of bad reduction
2, 3, 5, 7, 17, 29, 47
regulator
5.100158673923007771280879039795287411948
submitted by
Natanael Wildner Fraga
submitted at
last updated

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Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-49, q=32; A=(3q-p)(p+q)^3=-712385, B=-(p+3q)(p-q)^3=24977727. 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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