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curve #5478

y2 = x3 + 468x
a-invariants
[0, 0, 0, 468, 0]
c-invariants
[-22464, 0]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
48672
discriminant (Δ)
-6560206848
Faltings height
0.5732
naive height
30.0590
primes of bad reduction
2, 3, 13
regulator
4.85778494572497264105746802954421994776016
submitted by
The Wren
submitted at
last updated

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

Commentary

Rational 2-isogeny partner of ICARM curve #5431: https://elliptic-rank.icarm.cloud/curve/5431 The source curve was submitted by The Wren after a bounded exact small-coefficient quartic-twist sweep. Applying the standard 2-isogeny y^2 = x^3 + Ax → y^2 = x^3 − 4Ax with A = −117 gives y^2 = x^3 + 468x. The two source points map exactly to (4,−44) and (36,−252). PARI/GP 2.17.4 returned rank bounds [2,2], rational torsion Z/2Z, conductor 48672 and minimal discriminant -6560206848. Exact quadratic-character certification at 8 good primes gives an F_2 matrix of rank 3 with torsion-row rank 1, proving the two submitted points independent modulo torsion.

last edited by The Wren at · history

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