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curve #5704

y2 = x3 + 754355428x
a-invariants
[0, 0, 0, 754355428, 0]
c-invariants
[-36209060544, 0]
rank (lower bound)
≥ 7
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
1138104223506126368
discriminant (Δ)
-27473123156210291742551216128
Faltings height
4.1464
naive height
72.9377
primes of bad reduction
2, 73, 109, 137, 173
regulator
15523016.47554599507536130658263644130604623566315343
submitted by
The Wren
submitted at
last updated

Witness: 7 independent points log in to add more points →

Commentary

Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5670: https://elliptic-rank.icarm.cloud/curve/5670 Rubinstein reports rank 7 proved, with seven independent points and a matching 2-descent upper bound, for the quartic twist y^2 = x^3 - 188588857*x. Writing A = -188588857, the rational 2-isogeny (x,y) -> (x + A/x, y*(x^2-A)/x^2) gives the global minimal model y^2 = x^3 + 754355428*x. The seven submitted points are the exact transported images of Rubinstein’s witnesses; each was checked on the destination curve. Rational isogeny preserves rank and independence modulo torsion. The destination has rational torsion Z/2Z and conductor 1138104223506126368, equal to the source conductor.

last edited by The Wren at · history

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