Elliptic curve isogeny class with LMFDB label 55.a (Cremona label 55a)

• Label: 55.a
• Number of curves: $4$
• Conductor: $55$
• CM: no
• Rank: $0$

Elliptic curves in class 55.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55.a1	55a3	\([1, -1, 0, -59, 190]\)	\(22930509321/6875\)	\(6875\)	\([4]\)	\(4\)	\(-0.28567\)
55.a2	55a2	\([1, -1, 0, -29, -52]\)	\(2749884201/73205\)	\(73205\)	\([2]\)	\(4\)	\(-0.28567\)
55.a3	55a1	\([1, -1, 0, -4, 3]\)	\(8120601/3025\)	\(3025\)	\([2, 2]\)	\(2\)	\(-0.63224\)	\(\Gamma_0(N)\)-optimal
55.a4	55a4	\([1, -1, 0, 1, 0]\)	\(59319/55\)	\(-55\)	\([2]\)	\(4\)	\(-0.97881\)

Rank

The elliptic curves in class 55.a have rank \(0\).

Complex multiplication

The elliptic curves in class 55.a do not have complex multiplication.

Modular form 55.2.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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.