# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("9408.de1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.de

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.de1 9408de2 [0, 1, 0, -8801, -312033]  24576
9408.de2 9408de1 [0, 1, 0, 159, -16353]  12288 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form9408.2.a.de

sage: E.q_eigenform(10)

$$q + q^{3} + 4q^{5} + q^{9} - 4q^{11} + 4q^{13} + 4q^{15} - 4q^{19} + O(q^{20})$$

## 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. 