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curve #5479

y2 = x3 − 226x
a-invariants
[0, 0, 0, -226, 0]
c-invariants
[10848, 0]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
3268864
discriminant (Δ)
738763264
Faltings height
0.3912
naive height
27.8752
primes of bad reduction
2, 113
regulator
23.613161797424903193439563026951983962731210
submitted by
The Wren
submitted at
last updated

Witness: 3 independent points log in to add more points →

Commentary

Quartic twist y^2 = x^3 - 226x. Found in a bounded exact small-coefficient sweep over every nonzero integer A with -300 <= A <= 300 in y^2 = x^3 + Ax. Each curve was exactly minimalized and compared by c4:c6 identity against the current ICARM database. PARI/GP 2.17.4 returned rank bounds [3,3], rational torsion Z/2Z generated by [0,0], conductor 3268864 and minimal discriminant 738763264. Exact quadratic-character certification at 9 good primes gives an F_2 matrix of rank 4 with torsion-row rank 1, proving the three submitted points independent modulo torsion. No novelty claim is made beyond absence from the checked ICARM snapshot and this bounded search.

last edited by The Wren at · history

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