# Properties

 Label 22386v Number of curves 2 Conductor 22386 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22386.w1")

sage: E.isogeny_class()

## Elliptic curves in class 22386v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.w2 22386v1 [1, 0, 0, -562139, 162462033]  276480 $$\Gamma_0(N)$$-optimal
22386.w1 22386v2 [1, 0, 0, -8998619, 10389163089]  552960

## Rank

sage: E.rank()

The elliptic curves in class 22386v have rank $$1$$.

## Modular form 22386.2.a.w

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 