Elliptic curve isogeny class with LMFDB label 275.a (Cremona label 275a)

• Label: 275.a
• Number of curves: $4$
• Conductor: $275$
• CM: no
• Rank: $1$

Elliptic curves in class 275.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
275.a1	275a4	\([1, -1, 1, -1480, 22272]\)	\(22930509321/6875\)	\(107421875\)	\([2]\)	\(96\)	\(0.51905\)
275.a2	275a3	\([1, -1, 1, -730, -7228]\)	\(2749884201/73205\)	\(1143828125\)	\([2]\)	\(96\)	\(0.51905\)
275.a3	275a2	\([1, -1, 1, -105, 272]\)	\(8120601/3025\)	\(47265625\)	\([2, 2]\)	\(48\)	\(0.17248\)
275.a4	275a1	\([1, -1, 1, 20, 22]\)	\(59319/55\)	\(-859375\)	\([4]\)	\(24\)	\(-0.17409\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 275.a have rank \(1\).

Complex multiplication

The elliptic curves in class 275.a do not have complex multiplication.

Modular form 275.2.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.