# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.ct1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.ct1 9408bg3 [0, 1, 0, -6337, -196225] [2] 9216
9408.ct2 9408bg2 [0, 1, 0, -457, -2185] [2, 2] 4608
9408.ct3 9408bg1 [0, 1, 0, -212, 1098] [2] 2304 $$\Gamma_0(N)$$-optimal
9408.ct4 9408bg4 [0, 1, 0, 1503, -14337] [2] 9216

## Rank

sage: E.rank()

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

## Modular form9408.2.a.ct

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.