Elliptic curve isogeny class with Cremona label 23232cz (LMFDB label 23232.bo)

• Label: 23232cz
• Number of curves: $6$
• Conductor: $23232$
• CM: no
• Rank: $1$

Elliptic curves in class 23232cz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23232.bo5	23232cz1	$[0, -1, 0, 323, 2653]$	$2048/3$	$-5442235392$	$[2]$	$10240$	$0.55360$	$\Gamma_0(N)$-optimal
23232.bo4	23232cz2	$[0, -1, 0, -2097, 28305]$	$35152/9$	$261227298816$	$[2, 2]$	$20480$	$0.90017$
23232.bo3	23232cz3	$[0, -1, 0, -11777, -465375]$	$1556068/81$	$9404182757376$	$[2, 2]$	$40960$	$1.2467$
23232.bo2	23232cz4	$[0, -1, 0, -31137, 2124993]$	$28756228/3$	$348303065088$	$[2]$	$40960$	$1.2467$
23232.bo6	23232cz5	$[0, -1, 0, 7583, -1863167]$	$207646/6561$	$-1523477606694912$	$[2]$	$81920$	$1.5933$
23232.bo1	23232cz6	$[0, -1, 0, -186017, -30817983]$	$3065617154/9$	$2089818390528$	$[2]$	$81920$	$1.5933$

Rank

The elliptic curves in class 23232cz have rank $1$.

Complex multiplication

The elliptic curves in class 23232cz do not have complex multiplication.

Modular form 23232.2.a.cz

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.

$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.