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curve #2482

y2 + xy + y = x3 − x2 − 1525803593x + 10402419668681
a-invariants
[1, -1, 1, -1525803593, 10402419668681]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
377910
discriminant (Δ)
180596572914532407591724646400
Faltings height
4.3086
naive height
75.0510
primes of bad reduction
2, 3, 5, 13, 17, 19
regulator
2.957700008285857754826639498868651521750
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=-3, q=16; A=(3q-p)(p+q)^3=112047, B=-(p+3q)(p-q)^3=308655. 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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