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curve #2481

y2 + xy = x3 − 1725683455x + 26164676056025
a-invariants
[1, 0, 0, -1725683455, 26164676056025]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
1272810
discriminant (Δ)
33153377314362109938441000000
Faltings height
4.2262
naive height
75.4203
primes of bad reduction
2, 3, 5, 7, 11, 19, 29
regulator
2.272854417564613083905797161552345129036
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=-19, q=10; A=(3q-p)(p+q)^3=-35721, B=-(p+3q)(p-q)^3=268279. 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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