# Properties

 Label 221760ls Number of curves $4$ Conductor $221760$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ls1")

sage: E.isogeny_class()

## Elliptic curves in class 221760ls

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221760.cv4 221760ls1 $$[0, 0, 0, 13092, -552368]$$ $$20777545136/23059575$$ $$-275422087987200$$ $$[2]$$ $$524288$$ $$1.4573$$ $$\Gamma_0(N)$$-optimal
221760.cv3 221760ls2 $$[0, 0, 0, -74028, -5187152]$$ $$939083699236/300155625$$ $$14340158300160000$$ $$[2, 2]$$ $$1048576$$ $$1.8039$$
221760.cv2 221760ls3 $$[0, 0, 0, -470028, 120107248]$$ $$120186986927618/4332064275$$ $$413935187587891200$$ $$[2]$$ $$2097152$$ $$2.1504$$
221760.cv1 221760ls4 $$[0, 0, 0, -1071948, -427107728]$$ $$1425631925916578/270703125$$ $$25866086400000000$$ $$[2]$$ $$2097152$$ $$2.1504$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 221760ls do not have complex multiplication.

## Modular form 221760.2.a.ls

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.