# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.cu1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.cu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.cu1 9408bf2 [0, 1, 0, -177, 783] [2] 3072
9408.cu2 9408bf1 [0, 1, 0, -37, -85] [2] 1536 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form9408.2.a.cu

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + q^{9} - 2q^{11} - 4q^{13} + 2q^{15} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.