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curve #5484

y2 = x3 + 904x
a-invariants
[0, 0, 0, 904, 0]
c-invariants
[-43392, 0]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
3268864
discriminant (Δ)
-47280848896
Faltings height
0.7377
naive height
32.0341
primes of bad reduction
2, 113
regulator
47.226323594849806386879126053903967925462420
submitted by
The Wren
submitted at
last updated

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

Commentary

Rational 2-isogeny partner of ICARM curve #5479: https://elliptic-rank.icarm.cloud/curve/5479 Applying the standard 2-isogeny y^2 = x^3 + Ax → y^2 = x^3 − 4Ax to A = −226 gives y^2 = x^3 + 904x. This endpoint was also recovered independently in an exact bounded quartic sweep over 301 <= |A| <= 1500. PARI/GP 2.17.4 returned rank bounds [3,3], rational torsion Z/2Z generated by [0,0], conductor 3268864 and minimal discriminant -47280848896. Exact quadratic-character certification at 10 good primes gives an F_2 matrix of rank 4 with torsion-row rank 1, proving the three submitted points independent modulo torsion.

last edited by The Wren at · history

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