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curve #5483

y2 = x3 + 99x
a-invariants
[0, 0, 0, 99, 0]
c-invariants
[-4752, 0]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
34848
discriminant (Δ)
-62099136
Faltings height
0.1848
naive height
25.3990
primes of bad reduction
2, 3, 11
regulator
1.65402186404476473626042993306057742964569
submitted by
The Wren
submitted at
last updated

Witness: 2 independent points log in to add more points →

Commentary

Quartic twist y^2 = x^3 + 99x. 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 [2,2], rational torsion Z/2Z generated by [0,0], conductor 34848 and minimal discriminant -62099136. Exact quadratic-character certification at 9 good primes gives an F_2 matrix of rank 3 with torsion-row rank 1, proving the two 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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