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curve #2474

y2 + xy = x3 − x2 − 2927933415x + 60533270937225
a-invariants
[1, -1, 0, -2927933415, 60533270937225]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
3416490
discriminant (Δ)
23507163010132522151879240100
Faltings height
4.2691
naive height
77.0063
primes of bad reduction
2, 3, 5, 7, 11, 17, 29
regulator
2.885057393778513937692049962828471889818
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=-18, q=11; A=(3q-p)(p+q)^3=-17493, B=-(p+3q)(p-q)^3=365835. 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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