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curve #2479

y2 + xy = x3 − 15151153686x + 717811542849060
a-invariants
[1, 0, 0, -15151153686, 717811542849060]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
4829370
discriminant (Δ)
5604254832567097086286233600
Faltings height
4.4628
naive height
81.9376
primes of bad reduction
2, 3, 5, 7, 13, 29, 61
regulator
5.969763613136581258363480120736758757957
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=-13, q=16; A=(3q-p)(p+q)^3=1647, B=-(p+3q)(p-q)^3=853615. 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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