# Properties

 Label 9408.by Number of curves 2 Conductor 9408 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9408.by1")

sage: E.isogeny_class()

## Elliptic curves in class 9408.by

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.by1 9408bh2 [0, 1, 0, -49849, -4299289]  21504
9408.by2 9408bh1 [0, 1, 0, -3544, -48490]  10752 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form9408.2.a.by

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + q^{9} + 2q^{11} - 2q^{15} + 2q^{17} + O(q^{20})$$

## 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. 