# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("22386.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 22386.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22386.ba1 22386ba4 [1, 0, 0, -60253, -5035357]  124416
22386.ba2 22386ba2 [1, 0, 0, -14683, 682649]  41472
22386.ba3 22386ba1 [1, 0, 0, -643, 17153]  20736 $$\Gamma_0(N)$$-optimal
22386.ba4 22386ba3 [1, 0, 0, 5657, -408475]  62208

## Rank

sage: E.rank()

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

## Modular form 22386.2.a.ba

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 