# Properties

 Label 22050.ba Number of curves 6 Conductor 22050 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22050.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 22050.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.ba1 22050bi6 [1, -1, 0, -30103992, -63567163584] [2] 995328
22050.ba2 22050bi5 [1, -1, 0, -1879992, -994555584] [2] 497664
22050.ba3 22050bi4 [1, -1, 0, -391617, -77220459] [2] 331776
22050.ba4 22050bi2 [1, -1, 0, -115992, 15224166] [2] 110592
22050.ba5 22050bi1 [1, -1, 0, -5742, 340416] [2] 55296 $$\Gamma_0(N)$$-optimal
22050.ba6 22050bi3 [1, -1, 0, 49383, -7101459] [2] 165888

## Rank

sage: E.rank()

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

## Modular form 22050.2.a.ba

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.