Elliptic Curve Isogeny Class with LMFDB label 19.a (Cremona label 19a)

• Label: 19.a
• Number of curves: 3
• Conductor: 19
• CM: no
• Rank: 0

Elliptic curves in class 19.a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion order	Modular degree	Optimality
19.a1	19a2	[0, 1, 1, -769, -8470]	1	3
19.a2	19a1	[0, 1, 1, -9, -15]	3	1	\(\Gamma_0(N)\)-optimal
19.a3	19a3	[0, 1, 1, 1, 0]	3	3

Rank

The elliptic curves in class 19.a have rank \(0\).

Modular form 19.2.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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.