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curve #2492

y2 + xy + y = x3 − 672781938x + 6564320785156
a-invariants
[1, 0, 1, -672781938, 6564320785156]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
99330
discriminant (Δ)
874270039107335062500000000
Faltings height
3.9515
naive height
72.5944
primes of bad reduction
2, 3, 5, 7, 11, 43
regulator
2.985202424709282499024282063333352580372
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=-16, q=9; A=(3q-p)(p+q)^3=-14749, B=-(p+3q)(p-q)^3=171875. 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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