Elliptic curve isogeny class with Cremona label 2320d (LMFDB label 2320.f)

• Label: 2320d
• Number of curves: $4$
• Conductor: $2320$
• CM: no
• Rank: $1$

Elliptic curves in class 2320d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2320.f3	2320d1	$[0, 0, 0, -242, -1449]$	$97960237056/725$	$11600$	$[2]$	$256$	$-0.043745$	$\Gamma_0(N)$-optimal
2320.f2	2320d2	$[0, 0, 0, -247, -1386]$	$6509904336/525625$	$134560000$	$[2, 2]$	$512$	$0.30283$
2320.f1	2320d3	$[0, 0, 0, -827, 7546]$	$61085802564/11328125$	$11600000000$	$[4]$	$1024$	$0.64940$
2320.f4	2320d4	$[0, 0, 0, 253, -6286]$	$1748981916/17682025$	$-18106393600$	$[4]$	$1024$	$0.64940$

Rank

The elliptic curves in class 2320d have rank $1$.

Complex multiplication

The elliptic curves in class 2320d do not have complex multiplication.

Modular form 2320.2.a.d

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.