# Properties

 Label 22050bn Number of curves $2$ Conductor $22050$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22050.n1")

sage: E.isogeny_class()

## Elliptic curves in class 22050bn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.n2 22050bn1 [1, -1, 0, 3708, 113616] [] 48384 $$\Gamma_0(N)$$-optimal
22050.n1 22050bn2 [1, -1, 0, -35667, -4493259] [] 145152

## Rank

sage: E.rank()

The elliptic curves in class 22050bn have rank $$1$$.

## Modular form 22050.2.a.n

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 3q^{11} - q^{13} + q^{16} + 6q^{17} + q^{19} + O(q^{20})$$

## 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. 