# Properties

 Label 9408.be Number of curves $4$ Conductor $9408$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.be1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.be1 9408i3 [0, -1, 0, -790337, -270174015]  73728
9408.be2 9408i4 [0, -1, 0, -76897, 1010017]  73728
9408.be3 9408i2 [0, -1, 0, -49457, -4198095] [2, 2] 36864
9408.be4 9408i1 [0, -1, 0, -1437, -135603]  18432 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form9408.2.a.be

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 