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curve #2343

y2 + xy = x3 − x2 − 312417076869x + 32875181710420833
a-invariants
[1, -1, 0, -312417076869, 32875181710420833]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
32930370
discriminant (Δ)
1484676911001742579391069540039062500
Faltings height
5.6365
naive height
91.0164
primes of bad reduction
2, 3, 5, 11, 29, 31, 37
regulator
4.781664106779315518806568895491016013929
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=-6, q=31; A=(3q-p)(p+q)^3=1546875, B=-(p+3q)(p-q)^3=4406811. 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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