# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.cy1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.cy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.cy1 9408bd3 [0, 1, 0, -29857, -1993153] [2] 24576
9408.cy2 9408bd2 [0, 1, 0, -2417, -11985] [2, 2] 12288
9408.cy3 9408bd1 [0, 1, 0, -1437, 20355] [2] 6144 $$\Gamma_0(N)$$-optimal
9408.cy4 9408bd4 [0, 1, 0, 9343, -84897] [2] 24576

## Rank

sage: E.rank()

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

## Modular form9408.2.a.cy

sage: E.q_eigenform(10)

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

## 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.