# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22050.eh1")

sage: E.isogeny_class()

## Elliptic curves in class 22050.eh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.eh1 22050da3 [1, -1, 1, -514730, 124681897] [2] 331776
22050.eh2 22050da1 [1, -1, 1, -128855, -17748853] [2] 110592 $$\Gamma_0(N)$$-optimal
22050.eh3 22050da2 [1, -1, 1, -92105, -28112353] [2] 221184
22050.eh4 22050da4 [1, -1, 1, 808270, 659173897] [2] 663552

## Rank

sage: E.rank()

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

## Modular form 22050.2.a.eh

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.