Elliptic curve isogeny class with LMFDB label 58080.f (Cremona label 58080bg)

• Label: 58080.f
• Number of curves: $4$
• Conductor: $58080$
• CM: no
• Rank: $1$

Elliptic curves in class 58080.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
58080.f1	58080bg4	$[0, -1, 0, -384336, -91579464]$	$6922005943112/185625$	$168369157440000$	$[2]$	$368640$	$1.8345$
58080.f2	58080bg3	$[0, -1, 0, -106641, 12137985]$	$18483505984/1976535$	$14342358307368960$	$[2]$	$368640$	$1.8345$
58080.f3	58080bg1	$[0, -1, 0, -24966, -1305720]$	$15179306176/2205225$	$250028198798400$	$[2, 2]$	$184320$	$1.4879$	$\Gamma_0(N)$-optimal
58080.f4	58080bg2	$[0, -1, 0, 41584, -7135500]$	$8767302328/29229255$	$-26512081007132160$	$[2]$	$368640$	$1.8345$

Rank

The elliptic curves in class 58080.f have rank $1$.

Complex multiplication

The elliptic curves in class 58080.f do not have complex multiplication.

Modular form 58080.2.a.f

Isogeny matrix

The $i,j$ entry is the smallest degree of a cyclic isogeny between the $i$-th and $j$-th curve in the isogeny class, in the LMFDB numbering.

$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.