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curve #3749

y2 + xy = x3 − 1523953644x + 20076482101599
a-invariants
[1, 0, 0, -1523953644, 20076482101599]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ × ℤ/4ℤ
conductor (N)
7422373389
discriminant (Δ)
52387761033171861516056807649 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 4
Faltings height
4.2383 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 4
naive height
75.0473
primes of bad reduction
3, 19, 313, 541, 769
regulator
1558.787641393485903610636023106360846845144970
submitted by
Daniel Błażewicz
submitted at
last updated

Witness: 4 independent points log in to add more points →

Commentary

(u,v) = (541,228) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 4.

last edited by Daniel Błażewicz at · history

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