# Properties

 Label 9408.bj Number of curves 4 Conductor 9408 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.bj1 9408k3 [0, -1, 0, -6337, 196225]  9216
9408.bj2 9408k2 [0, -1, 0, -457, 2185] [2, 2] 4608
9408.bj3 9408k1 [0, -1, 0, -212, -1098]  2304 $$\Gamma_0(N)$$-optimal
9408.bj4 9408k4 [0, -1, 0, 1503, 14337]  9216

## Rank

sage: E.rank()

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

## Modular form9408.2.a.bj

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 