Elliptic curve isogeny class with Cremona label 17a (LMFDB label 17.a)

• Label: 17a
• Number of curves: $4$
• Conductor: $17$
• CM: no
• Rank: $0$

Elliptic curves in class 17a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17.a3	17a1	$[1, -1, 1, -1, -14]$	$-35937/83521$	$-83521$	$[4]$	$1$	$-0.37664$	$\Gamma_0(N)$-optimal
17.a2	17a2	$[1, -1, 1, -6, -4]$	$20346417/289$	$289$	$[2, 2]$	$2$	$-0.72321$
17.a1	17a3	$[1, -1, 1, -91, -310]$	$82483294977/17$	$17$	$[2]$	$4$	$-0.37664$
17.a4	17a4	$[1, -1, 1, -1, 0]$	$35937/17$	$17$	$[4]$	$4$	$-1.0698$

Rank

The elliptic curves in class 17a have rank $0$.

Complex multiplication

The elliptic curves in class 17a do not have complex multiplication.

Modular form 17.2.a.a

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.