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curve #2273

y2 + xy = x3 − 3965841176011x + 2685455277921127985
a-invariants
[1, 0, 0, -3965841176011, 2685455277921127985]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
213913830
discriminant (Δ)
876515435347371617662633273477925160000
Faltings height
6.2015
naive height
98.6398
primes of bad reduction
2, 3, 5, 13, 53, 79, 131
regulator
6.309807565176830804613734950306863828532
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=-53, q=26; A=(3q-p)(p+q)^3=-2578473, B=-(p+3q)(p-q)^3=12325975. 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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