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curve #2360

y2 + xy = x3 − 211259358976x − 33984101803294720
a-invariants
[1, 0, 0, -211259358976, -33984101803294720]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
18853890
discriminant (Δ)
104506752225180137953045566298521600
Faltings height
5.4558
naive height
89.8427
primes of bad reduction
2, 3, 5, 11, 19, 31, 97
regulator
5.189794376152759453580775800624947687228
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=-1, q=32; A=(3q-p)(p+q)^3=2889727, B=-(p+3q)(p-q)^3=3414015. 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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