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

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

Elliptic curves in class 1710.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1710.o1	1710o4	$[1, -1, 1, -67298, 6505697]$	$46237740924063961/1806561830400$	$1316983574361600$	$[6]$	$6912$	$1.6684$
1710.o2	1710o2	$[1, -1, 1, -9923, -375253]$	$148212258825961/1218375000$	$888195375000$	$[2]$	$2304$	$1.1191$
1710.o3	1710o1	$[1, -1, 1, -203, -13669]$	$-1263214441/110808000$	$-80779032000$	$[2]$	$1152$	$0.77253$	$\Gamma_0(N)$-optimal
1710.o4	1710o3	$[1, -1, 1, 1822, 367841]$	$918046641959/80912056320$	$-58984889057280$	$[6]$	$3456$	$1.3218$

Rank

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

Complex multiplication

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

Modular form 1710.2.a.o

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.

$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.