# Properties

 Label 9408.ce Number of curves 2 Conductor 9408 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.ce1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.ce1 9408v2 [0, 1, 0, -442241, -117590817] [] 112896
9408.ce2 9408v1 [0, 1, 0, -3201, 159711] [] 16128 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9408.ce have rank $$0$$.

## Modular form9408.2.a.ce

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - 5q^{11} - q^{15} - 4q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 