# Properties

 Label 22386i Number of curves 4 Conductor 22386 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22386.m1")

sage: E.isogeny_class()

## Elliptic curves in class 22386i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.m4 22386i1 [1, 0, 1, -575, 914]  17280 $$\Gamma_0(N)$$-optimal
22386.m2 22386i2 [1, 0, 1, -5695, -164974] [2, 2] 34560
22386.m3 22386i3 [1, 0, 1, -2335, -357166]  69120
22386.m1 22386i4 [1, 0, 1, -90975, -10569134]  69120

## Rank

sage: E.rank()

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

## Modular form 22386.2.a.m

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 