# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("22050.j1")

sage: E.isogeny_class()

## Elliptic curves in class 22050cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.j2 22050cb1 [1, -1, 0, -24117, 6336791] [] 161280 $$\Gamma_0(N)$$-optimal
22050.j1 22050cb2 [1, -1, 0, -75269742, -251331415084] [] 2096640

## Rank

sage: E.rank()

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

## Modular form 22050.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 3q^{11} - 5q^{13} + q^{16} + 2q^{17} - 5q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 