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curve #2528

y2 + xy + y = x3 − 945023349x + 11181724897516
a-invariants
[1, 0, 1, -945023349, 11181724897516]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
2284590
discriminant (Δ)
14861562168273888860100
Faltings height
3.6574
naive height
73.6138
primes of bad reduction
2, 3, 5, 7, 11, 23, 43
regulator
2.809706369678720430065612753285658834242
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=-10, q=11; A=(3q-p)(p+q)^3=43, B=-(p+3q)(p-q)^3=213003. 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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