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curve #2569

y2 + xy = x3 − 12180181x + 16360637345
a-invariants
[1, 0, 0, -12180181, 16360637345]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
30030
discriminant (Δ)
834505270358760000
Faltings height
2.6478
naive height
60.5596
primes of bad reduction
2, 3, 5, 7, 11, 13
regulator
3.270112321583608897548806044893333846473
submitted by
Natanael Wildner Fraga
submitted at
last updated

Witness: 1 independent point log in to add more points →

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-25, q=1; A=(3q-p)(p+q)^3=-387072, B=-(p+3q)(p-q)^3=-386672. 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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