Elliptic curve isogeny class with LMFDB label 15.a (Cremona label 15a)

• Label: 15.a
• Number of curves: $8$
• Conductor: $15$
• CM: no
• Rank: $0$

Elliptic curves in class 15.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15.a1	15a5	\([1, 1, 1, -2160, -39540]\)	\(1114544804970241/405\)	\(405\)	\([2]\)	\(4\)	\(0.29087\)
15.a2	15a2	\([1, 1, 1, -135, -660]\)	\(272223782641/164025\)	\(164025\)	\([2, 2]\)	\(2\)	\(-0.055704\)
15.a3	15a6	\([1, 1, 1, -110, -880]\)	\(-147281603041/215233605\)	\(-215233605\)	\([2]\)	\(4\)	\(0.29087\)
15.a4	15a7	\([1, 1, 1, -80, 242]\)	\(56667352321/15\)	\(15\)	\([4]\)	\(4\)	\(-0.40228\)
15.a5	15a1	\([1, 1, 1, -10, -10]\)	\(111284641/50625\)	\(50625\)	\([2, 4]\)	\(1\)	\(-0.40228\)	\(\Gamma_0(N)\)-optimal
15.a6	15a3	\([1, 1, 1, -5, 2]\)	\(13997521/225\)	\(225\)	\([2, 4]\)	\(2\)	\(-0.74885\)
15.a7	15a8	\([1, 1, 1, 0, 0]\)	\(-1/15\)	\(-15\)	\([4]\)	\(4\)	\(-1.0954\)
15.a8	15a4	\([1, 1, 1, 35, -28]\)	\(4733169839/3515625\)	\(-3515625\)	\([8]\)	\(2\)	\(-0.055704\)

Rank

The elliptic curves in class 15.a have rank \(0\).

Complex multiplication

The elliptic curves in class 15.a do not have complex multiplication.

Modular form 15.2.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.