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curve #2291

y2 + xy + y = x3 − x2 − 1803769728287x + 924519212929720199
a-invariants
[1, -1, 1, -1803769728287, 924519212929720199]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
1711710
discriminant (Δ)
6352492644226678205708502994944000000
Faltings height
5.8811
naive height
96.2763
primes of bad reduction
2, 3, 5, 7, 11, 13, 19
regulator
3.409857796625362971005525103039801007602
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=-57, q=8; A=(3q-p)(p+q)^3=-9529569, B=-(p+3q)(p-q)^3=-9062625. 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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