# Properties

 Label 346560.io Number of curves $2$ Conductor $346560$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("346560.io1")

sage: E.isogeny_class()

## Elliptic curves in class 346560.io

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
346560.io1 346560io2 [0, 1, 0, -616496065, 5876559797663]  224133120
346560.io2 346560io1 [0, 1, 0, -54606785, 7851023775]  112066560 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 346560.io have rank $$1$$.

## Modular form 346560.2.a.io

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 4q^{7} + q^{9} - 6q^{11} - 4q^{13} + q^{15} + 6q^{17} + O(q^{20})$$

## 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. 