Elliptic curve isogeny class with Cremona label 346560e (LMFDB label 346560.e)

• Label: 346560e
• Number of curves: $4$
• Conductor: $346560$
• CM: no
• Rank: $1$

Elliptic curves in class 346560e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
346560.e4	346560e1	$[0, -1, 0, 1324, -197574]$	$85184/5625$	$-16936517160000$	$[2]$	$921600$	$1.2180$	$\Gamma_0(N)$-optimal
346560.e3	346560e2	$[0, -1, 0, -43801, -3383399]$	$48228544/2025$	$390217355366400$	$[2, 2]$	$1843200$	$1.5645$
346560.e2	346560e3	$[0, -1, 0, -116001, 10724481]$	$111980168/32805$	$50572169255485440$	$[2]$	$3686400$	$1.9111$
346560.e1	346560e4	$[0, -1, 0, -693601, -222106079]$	$23937672968/45$	$69371974287360$	$[2]$	$3686400$	$1.9111$

Rank

The elliptic curves in class 346560e have rank $1$.

Complex multiplication

The elliptic curves in class 346560e do not have complex multiplication.

Modular form 346560.2.a.e

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.