# Properties

 Label 221067.y Number of curves $2$ Conductor $221067$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 221067.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.y1 221067bb2 $$[1, -1, 0, -168273, 26610700]$$ $$408023180713/1421$$ $$1835175983949$$ $$[2]$$ $$737280$$ $$1.5726$$
221067.y2 221067bb1 $$[1, -1, 0, -10368, 430051]$$ $$-95443993/5887$$ $$-7602871933503$$ $$[2]$$ $$368640$$ $$1.2260$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 221067.y have rank $$1$$.

## Complex multiplication

The elliptic curves in class 221067.y do not have complex multiplication.

## Modular form 221067.2.a.y

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 2q^{5} - q^{7} - 3q^{8} - 2q^{10} + 2q^{13} - q^{14} - q^{16} + 4q^{17} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.