# Properties

 Label 22050.cj Number of curves $4$ Conductor $22050$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cj1")

sage: E.isogeny_class()

## Elliptic curves in class 22050.cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.cj1 22050bq4 [1, -1, 0, -4118067, 3217561591] [2] 589824
22050.cj2 22050bq2 [1, -1, 0, -259317, 49527841] [2, 2] 294912
22050.cj3 22050bq1 [1, -1, 0, -38817, -1848659] [2] 147456 $$\Gamma_0(N)$$-optimal
22050.cj4 22050bq3 [1, -1, 0, 71433, 166944091] [2] 589824

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 22050.cj do not have complex multiplication.

## Modular form 22050.2.a.cj

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.