# Properties

 Label 9680.q Number of curves 4 Conductor 9680 CM no Rank 1 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("9680.q1")

sage: E.isogeny_class()

## Elliptic curves in class 9680.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9680.q1 9680h3 [0, 0, 0, -12947, -567006] [2] 10240
9680.q2 9680h2 [0, 0, 0, -847, -7986] [2, 2] 5120
9680.q3 9680h1 [0, 0, 0, -242, 1331] [2] 2560 $$\Gamma_0(N)$$-optimal
9680.q4 9680h4 [0, 0, 0, 1573, -45254] [2] 10240

## Rank

sage: E.rank()

The elliptic curves in class 9680.q have rank $$1$$.

## Modular form9680.2.a.q

sage: E.q_eigenform(10)

$$q + q^{5} - 4q^{7} - 3q^{9} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().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.

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

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.