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curve #2289

y2 + xy + y = x3 − 1888683281469x + 792253530598687876
a-invariants
[1, 0, 1, -1888683281469, 792253530598687876]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
57960870
discriminant (Δ)
160027111096058562029170232707376568900
Faltings height
6.0449
naive height
96.4143
primes of bad reduction
2, 3, 5, 11, 37, 47, 101
regulator
4.525299837675477751903465916915758487107
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=-10, q=37; A=(3q-p)(p+q)^3=2381643, B=-(p+3q)(p-q)^3=10486123. 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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