# Properties

 Label 9408.cl Number of curves $2$ Conductor $9408$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.cl1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.cl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.cl1 9408y2 [0, 1, 0, -513, 3807] [2] 4096
9408.cl2 9408y1 [0, 1, 0, 47, 335] [2] 2048 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9408.cl have rank $$1$$.

## Modular form9408.2.a.cl

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.