Elliptic curve isogeny class with Cremona label 24640z (LMFDB label 24640.q)

• Label: 24640z
• Number of curves: $4$
• Conductor: $24640$
• CM: no
• Rank: $0$

Elliptic curves in class 24640z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
24640.q4	24640z1	$[0, 0, 0, -188, -2448]$	$-44851536/132055$	$-2163589120$	$[2]$	$8192$	$0.47816$	$\Gamma_0(N)$-optimal
24640.q3	24640z2	$[0, 0, 0, -4108, -101232]$	$116986321764/148225$	$9714073600$	$[2, 2]$	$16384$	$0.82474$
24640.q2	24640z3	$[0, 0, 0, -5228, -41648]$	$120564797922/64054375$	$8395735040000$	$[2]$	$32768$	$1.1713$
24640.q1	24640z4	$[0, 0, 0, -65708, -6482992]$	$239369344910082/385$	$50462720$	$[2]$	$32768$	$1.1713$

Rank

The elliptic curves in class 24640z have rank $0$.

Complex multiplication

The elliptic curves in class 24640z do not have complex multiplication.

Modular form 24640.2.a.z

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.