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curve #5705

y2 = x3 + 580080664x
a-invariants
[0, 0, 0, 580080664, 0]
c-invariants
[-27843871872, 0]
rank (lower bound)
≥ 7
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
1345974306986723584
discriminant (Δ)
-12492378715580775292658876416
Faltings height
4.0807
naive height
72.1496
primes of bad reduction
2, 17, 43, 281, 353
regulator
21445971.51718009398309453496004516316720651221274281
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 #5671: https://elliptic-rank.icarm.cloud/curve/5671 Rubinstein reports rank 7 proved, with seven independent points and a matching 2-descent upper bound, for the quartic twist y^2 = x^3 - 145020166*x. Writing A = -145020166, the rational 2-isogeny (x,y) -> (x + A/x, y*(x^2-A)/x^2) gives the global minimal model y^2 = x^3 + 580080664*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 1345974306986723584, equal to the source conductor.

last edited by The Wren at · history

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