Elliptic curve isogeny class with Cremona label 9680h (LMFDB label 9680.q)

• Label: 9680h
• Number of curves: $4$
• Conductor: $9680$
• CM: no
• Rank: $1$

Elliptic curves in class 9680h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9680.q3	9680h1	\([0, 0, 0, -242, 1331]\)	\(55296/5\)	\(141724880\)	\([2]\)	\(2560\)	\(0.30359\)	\(\Gamma_0(N)\)-optimal
9680.q2	9680h2	\([0, 0, 0, -847, -7986]\)	\(148176/25\)	\(11337990400\)	\([2, 2]\)	\(5120\)	\(0.65016\)
9680.q1	9680h3	\([0, 0, 0, -12947, -567006]\)	\(132304644/5\)	\(9070392320\)	\([2]\)	\(10240\)	\(0.99673\)
9680.q4	9680h4	\([0, 0, 0, 1573, -45254]\)	\(237276/625\)	\(-1133799040000\)	\([2]\)	\(10240\)	\(0.99673\)

Rank

The elliptic curves in class 9680h have rank \(1\).

Complex multiplication

The elliptic curves in class 9680h do not have complex multiplication.

Modular form 9680.2.a.h

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.