# Properties

 Label 22050z Number of curves $2$ Conductor $22050$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22050.i1")

sage: E.isogeny_class()

## Elliptic curves in class 22050z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.i1 22050z1 [1, -1, 0, -358542, -185734634] [] 580608 $$\Gamma_0(N)$$-optimal
22050.i2 22050z2 [1, -1, 0, 3114333, 4110211741] [] 1741824

## Rank

sage: E.rank()

The elliptic curves in class 22050z have rank $$0$$.

## Modular form 22050.2.a.i

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 3q^{11} - 5q^{13} + q^{16} + 5q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 