# Properties

 Label 221760.fl Number of curves 4 Conductor 221760 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("221760.fl1")

sage: E.isogeny_class()

## Elliptic curves in class 221760.fl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221760.fl1 221760de3 [0, 0, 0, -19002828, 31883804048] [2] 9437184
221760.fl2 221760de2 [0, 0, 0, -1221708, 468121232] [2, 2] 4718592
221760.fl3 221760de1 [0, 0, 0, -288588, -51813232] [2] 2359296 $$\Gamma_0(N)$$-optimal
221760.fl4 221760de4 [0, 0, 0, 1629492, 2328244112] [2] 9437184

## Rank

sage: E.rank()

The elliptic curves in class 221760.fl have rank $$1$$.

## Modular form 221760.2.a.fl

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.