# Properties

 Label 160080.l Number of curves 2 Conductor 160080 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("160080.l1")
sage: E.isogeny_class()

## Elliptic curves in class 160080.l

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
160080.l1 160080bx1 [0, -1, 0, -5976, -175824] 2 110592 $$\Gamma_0(N)$$-optimal
160080.l2 160080bx2 [0, -1, 0, -5576, -200784] 2 221184

## Rank

sage: E.rank()

The elliptic curves in class 160080.l have rank $$0$$.

## Modular form 160080.2.a.l

sage: E.q_eigenform(10)
$$q - q^{3} - q^{5} + q^{9} - 2q^{11} + 2q^{13} + q^{15} - 4q^{17} + O(q^{20})$$

## 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.