Elliptic curve isogeny class with LMFDB label 232050.dz (Cremona label 232050dz)

• Label: 232050.dz
• Number of curves: $4$
• Conductor: $232050$
• CM: no
• Rank: $1$

Elliptic curves in class 232050.dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
232050.dz1	232050dz3	$[1, 1, 1, -5065438, 4385588531]$	$919929834039591549721/90169756021800$	$1408902437840625000$	$[2]$	$8847360$	$2.5178$
232050.dz2	232050dz4	$[1, 1, 1, -1887438, -951155469]$	$47590666162724706841/2569185084375000$	$40143516943359375000$	$[2]$	$8847360$	$2.5178$
232050.dz3	232050dz2	$[1, 1, 1, -340438, 57488531]$	$279265866686253721/69785974440000$	$1090405850625000000$	$[2, 2]$	$4423680$	$2.1712$
232050.dz4	232050dz1	$[1, 1, 1, 51562, 5744531]$	$970269597296999/1467060940800$	$-22922827200000000$	$[2]$	$2211840$	$1.8246$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 232050.dz have rank $1$.

Complex multiplication

The elliptic curves in class 232050.dz do not have complex multiplication.

Modular form 232050.2.a.dz

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.