# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 9408g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.w1 9408g1 [0, -1, 0, -408, -2862]  3072 $$\Gamma_0(N)$$-optimal
9408.w2 9408g2 [0, -1, 0, 327, -12711]  6144

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form9408.2.a.g

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 