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curve #2428

y2 + xy + y = x3 − 26257551129x + 1627223558303656
a-invariants
[1, 0, 1, -26257551129, 1627223558303656]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
52052970
discriminant (Δ)
14747213612354834443742767844100
Faltings height
4.8116
naive height
83.5873
primes of bad reduction
2, 3, 5, 19, 29, 47, 67
regulator
10.05450662232241969049359423145334636133
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=19; A=(3q-p)(p+q)^3=48843, B=-(p+3q)(p-q)^3=1146283. 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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