# Properties

 Label 22386.y Number of curves 2 Conductor 22386 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22386.y1")

sage: E.isogeny_class()

## Elliptic curves in class 22386.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.y1 22386w1 [1, 0, 0, -155806, 23664452] [7] 131712 $$\Gamma_0(N)$$-optimal
22386.y2 22386w2 [1, 0, 0, 864584, -1045089598] [] 921984

## Rank

sage: E.rank()

The elliptic curves in class 22386.y have rank $$0$$.

## Modular form 22386.2.a.y

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 2q^{11} + q^{12} - q^{13} + q^{14} - q^{15} + q^{16} + 4q^{17} + q^{18} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.