# Properties

 Label 22386.n Number of curves 4 Conductor 22386 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22386.n1")

sage: E.isogeny_class()

## Elliptic curves in class 22386.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.n1 22386m4 [1, 0, 1, -1485, 20986]  31232
22386.n2 22386m2 [1, 0, 1, -255, -1154] [2, 2] 15616
22386.n3 22386m1 [1, 0, 1, -235, -1402]  7808 $$\Gamma_0(N)$$-optimal
22386.n4 22386m3 [1, 0, 1, 655, -7342]  31232

## Rank

sage: E.rank()

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

## Modular form 22386.2.a.n

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 