# Properties

 Label 9408.u Number of curves $2$ Conductor $9408$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.u1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.u1 9408e2 [0, -1, 0, -25153, -1356095]  28672
9408.u2 9408e1 [0, -1, 0, 2287, -110319]  14336 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form9408.2.a.u

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 