# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 221067.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221067.c1 221067c2 [1, -1, 1, -18041, -864894] [2] 442368
221067.c2 221067c1 [1, -1, 1, -3686, 71052] [2] 221184 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 221067.c have rank $$2$$.

## Complex multiplication

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

## Modular form 221067.2.a.c

sage: E.q_eigenform(10)

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

## 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.