# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("346560.fp1")

sage: E.isogeny_class()

## Elliptic curves in class 346560fp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
346560.fp2 346560fp1 [0, -1, 0, -54606785, -7851023775]  112066560 $$\Gamma_0(N)$$-optimal
346560.fp1 346560fp2 [0, -1, 0, -616496065, -5876559797663]  224133120

## Rank

sage: E.rank()

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

## Modular form 346560.2.a.fp

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 Cremona 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 Cremona labels. 