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curve #2467

y2 + xy = x3 − 3765611966x + 4923182213700
a-invariants
[1, 0, 0, -3765611966, 4923182213700]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
11942490
discriminant (Δ)
3406856008675291207692720537600
Faltings height
4.5481
naive height
77.7611
primes of bad reduction
2, 3, 5, 7, 29, 37, 53
regulator
4.048742229560287019791479125189150124653
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=-29, q=8; A=(3q-p)(p+q)^3=-490833, B=-(p+3q)(p-q)^3=-253265. 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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