Elliptic curve isogeny class with LMFDB label 45.a (Cremona label 45a)

• Label: 45.a
• Number of curves: $8$
• Conductor: $45$
• CM: no
• Rank: $0$

Elliptic curves in class 45.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
45.a1	45a7	\([1, -1, 0, -19440, 1048135]\)	\(1114544804970241/405\)	\(295245\)	\([2]\)	\(32\)	\(0.84018\)
45.a2	45a5	\([1, -1, 0, -1215, 16600]\)	\(272223782641/164025\)	\(119574225\)	\([2, 2]\)	\(16\)	\(0.49360\)
45.a3	45a8	\([1, -1, 0, -990, 22765]\)	\(-147281603041/215233605\)	\(-156905298045\)	\([2]\)	\(32\)	\(0.84018\)
45.a4	45a3	\([1, -1, 0, -720, -7259]\)	\(56667352321/15\)	\(10935\)	\([2]\)	\(8\)	\(0.14703\)
45.a5	45a4	\([1, -1, 0, -90, 175]\)	\(111284641/50625\)	\(36905625\)	\([2, 2]\)	\(8\)	\(0.14703\)
45.a6	45a2	\([1, -1, 0, -45, -104]\)	\(13997521/225\)	\(164025\)	\([2, 2]\)	\(4\)	\(-0.19954\)
45.a7	45a1	\([1, -1, 0, 0, -5]\)	\(-1/15\)	\(-10935\)	\([2]\)	\(2\)	\(-0.54612\)	\(\Gamma_0(N)\)-optimal
45.a8	45a6	\([1, -1, 0, 315, 1066]\)	\(4733169839/3515625\)	\(-2562890625\)	\([2]\)	\(16\)	\(0.49360\)

Rank

The elliptic curves in class 45.a have rank \(0\).

Complex multiplication

The elliptic curves in class 45.a do not have complex multiplication.

Modular form 45.2.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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.