# Properties

 Label 22386.bc Number of curves 4 Conductor 22386 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22386.bc1")

sage: E.isogeny_class()

## Elliptic curves in class 22386.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.bc1 22386x4 [1, 0, 0, -3684097, -2722034887] [2] 344064
22386.bc2 22386x3 [1, 0, 0, -237537, -39713895] [2] 344064
22386.bc3 22386x2 [1, 0, 0, -230257, -42545815] [2, 2] 172032
22386.bc4 22386x1 [1, 0, 0, -13937, -709527] [2] 86016 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 22386.2.a.bc

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.