# Properties

 Label 346560.lg Number of curves $2$ Conductor $346560$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("346560.lg1")

sage: E.isogeny_class()

## Elliptic curves in class 346560.lg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
346560.lg1 346560lg2 [0, 1, 0, -1707745, 856226975] [2] 11796480
346560.lg2 346560lg1 [0, 1, 0, -151265, 1096863] [2] 5898240 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 346560.lg have rank $$0$$.

## Modular form 346560.2.a.lg

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.