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curve #2485

y2 + xy + y = x3 − 1037754439x + 3530918635286
a-invariants
[1, 0, 1, -1037754439, 3530918635286]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
930930
discriminant (Δ)
66139797949925005619409996900
Faltings height
4.2214
naive height
73.8946
primes of bad reduction
2, 3, 5, 7, 11, 13, 31
regulator
2.292188085496054138440363017464888796178
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=-22, q=9; A=(3q-p)(p+q)^3=-107653, B=-(p+3q)(p-q)^3=148955. 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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