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	Torsion structure	Modular degree	Optimality
17.a3	17a1	[1, -1, 1, -1, -14]	[4]	1	\(\Gamma_0(N)\)-optimal
17.a2	17a2	[1, -1, 1, -6, -4]	[2, 2]	2
17.a1	17a3	[1, -1, 1, -91, -310]	[2]	4
17.a4	17a4	[1, -1, 1, -1, 0]	[4]	4

Rank

The elliptic curves in class 17a have rank \(0\).

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.