# Properties

 Label 9408.r Number of curves 4 Conductor 9408 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.r1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.r1 9408bw4 [0, -1, 0, -358353, -82449135] [2] 55296
9408.r2 9408bw3 [0, -1, 0, -22213, -1304939] [2] 27648
9408.r3 9408bw2 [0, -1, 0, -5553, -49167] [2] 18432
9408.r4 9408bw1 [0, -1, 0, 1307, -6635] [2] 9216 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form9408.2.a.r

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.