# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("9408.bf1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.bf1 9408cb2 [0, -1, 0, -177, -783]  3072
9408.bf2 9408cb1 [0, -1, 0, -37, 85]  1536 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form9408.2.a.bf

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. 