# Properties

 Label 9408.b Number of curves $2$ Conductor $9408$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.b1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.b1 9408ch2 [0, -1, 0, -431265, 106164801]  172032
9408.b2 9408ch1 [0, -1, 0, 7775, 5624641]  86016 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form9408.2.a.b

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. 