# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 9408c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.bg2 9408c1 [0, -1, 0, -457, 4243] [] 3360 $$\Gamma_0(N)$$-optimal
9408.bg1 9408c2 [0, -1, 0, -178817, -29068437] [] 43680

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 9408c do not have complex multiplication.

## Modular form9408.2.a.c

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.