# Properties

 Label 22050.bm Number of curves $4$ Conductor $22050$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22050.bm1")

sage: E.isogeny_class()

## Elliptic curves in class 22050.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.bm1 22050d3 [1, -1, 0, -1159692, 480378716] [2] 331776
22050.bm2 22050d4 [1, -1, 0, -828942, 759862466] [2] 663552
22050.bm3 22050d1 [1, -1, 0, -57192, -4598784] [2] 110592 $$\Gamma_0(N)$$-optimal
22050.bm4 22050d2 [1, -1, 0, 89808, -24443784] [2] 221184

## Rank

sage: E.rank()

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

## Modular form 22050.2.a.bm

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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.