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

• Label: 1710.c
• Number of curves: $2$
• Conductor: $1710$
• CM: no
• Rank: $1$

Elliptic curves in class 1710.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1710.c1	1710f2	$[1, -1, 0, -270, 1750]$	$2992209121/54150$	$39475350$	$[2]$	$768$	$0.25288$
1710.c2	1710f1	$[1, -1, 0, 0, 76]$	$-1/3420$	$-2493180$	$[2]$	$384$	$-0.093694$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1710.c have rank $1$.

Complex multiplication

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

Modular form 1710.2.a.c

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.

$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.