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curve #2678

y2 + xy = x3 − 442752806x + 3473504002020
a-invariants
[1, 0, 0, -442752806, 3473504002020]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
4537470
discriminant (Δ)
342452510559217619805081600
Faltings height
3.8619
naive height
71.3392
primes of bad reduction
2, 3, 5, 7, 17, 31, 41
regulator
6.56395219184902864681575020352277180538190
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=-5, q=12; A=(3q-p)(p+q)^3=14063, B=-(p+3q)(p-q)^3=152303. 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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