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

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

Elliptic curves in class 232050x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
232050.x3	232050x1	$[1, 1, 0, -4550, 52500]$	$666940371553/304152576$	$4752384000000$	$[2]$	$524288$	$1.1275$	$\Gamma_0(N)$-optimal
232050.x2	232050x2	$[1, 1, 0, -36550, -2667500]$	$345608484635233/5513953536$	$86155524000000$	$[2, 2]$	$1048576$	$1.4740$
232050.x4	232050x3	$[1, 1, 0, -2550, -7393500]$	$-117433042273/1510843540752$	$-23606930324250000$	$[2]$	$2097152$	$1.8206$
232050.x1	232050x4	$[1, 1, 0, -582550, -171381500]$	$1399279497274949473/364819728$	$5700308250000$	$[2]$	$2097152$	$1.8206$

Rank

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

Complex multiplication

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

Modular form 232050.2.a.x

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.