# Properties

 Label 9408.bw Number of curves $6$ Conductor $9408$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.bw1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.bw1 9408db4 [0, 1, 0, -4214849, 3329185215] [2] 147456
9408.bw2 9408db5 [0, 1, 0, -2866369, -1850890945] [2] 294912
9408.bw3 9408db3 [0, 1, 0, -326209, 25271231] [2, 2] 147456
9408.bw4 9408db2 [0, 1, 0, -263489, 51927231] [2, 2] 73728
9408.bw5 9408db1 [0, 1, 0, -12609, 1199295] [2] 36864 $$\Gamma_0(N)$$-optimal
9408.bw6 9408db6 [0, 1, 0, 1210431, 196452927] [2] 294912

## Rank

sage: E.rank()

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

## Modular form9408.2.a.bw

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.