Elliptic curve isogeny class with LMFDB label 1710.f (Cremona label 1710d)

• Label: 1710.f
• Number of curves: $4$
• Conductor: $1710$
• CM: no
• Rank: $0$

Elliptic curves in class 1710.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1710.f1	1710d3	$[1, -1, 0, -27360, -1735074]$	$3107086841064961/570$	$415530$	$[2]$	$3072$	$0.91382$
1710.f2	1710d4	$[1, -1, 0, -1980, -17550]$	$1177918188481/488703750$	$356265033750$	$[2]$	$3072$	$0.91382$
1710.f3	1710d2	$[1, -1, 0, -1710, -26784]$	$758800078561/324900$	$236852100$	$[2, 2]$	$1536$	$0.56725$
1710.f4	1710d1	$[1, -1, 0, -90, -540]$	$-111284641/123120$	$-89754480$	$[2]$	$768$	$0.22067$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1710.f have rank $0$.

Complex multiplication

The elliptic curves in class 1710.f do not have complex multiplication.

Modular form 1710.2.a.f

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.