# Properties

 Label 221760fa Number of curves 4 Conductor 221760 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("221760.dd1")

sage: E.isogeny_class()

## Elliptic curves in class 221760fa

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221760.dd3 221760fa1 [0, 0, 0, -32268, 43416592] [2] 2654208 $$\Gamma_0(N)$$-optimal
221760.dd2 221760fa2 [0, 0, 0, -2059788, 1127734288] [2] 5308416
221760.dd4 221760fa3 [0, 0, 0, 290292, -1169538032] [2] 7962624
221760.dd1 221760fa4 [0, 0, 0, -15042828, -21820184048] [2] 15925248

## Rank

sage: E.rank()

The elliptic curves in class 221760fa have rank $$0$$.

## Modular form 221760.2.a.dd

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.