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curve #2675

y2 + xy + y = x3 − 11907929323x + 500151545853506
a-invariants
[1, 0, 1, -11907929323, 500151545853506]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
11138610
discriminant (Δ)
4442413948011741267562500
Faltings height
4.2504
naive height
81.2150
primes of bad reduction
2, 3, 5, 7, 29, 31, 59
regulator
22.7176705888064883538397324876603411827828
submitted by
Natanael Wildner Fraga
submitted at
last updated

Witness: 2 independent points log in to add more points →

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-14, q=15; A=(3q-p)(p+q)^3=59, B=-(p+3q)(p-q)^3=756059. 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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