# Properties

 Label 227430.x Number of curves $2$ Conductor $227430$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("227430.x1")

sage: E.isogeny_class()

## Elliptic curves in class 227430.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.x1 227430fy2 [1, -1, 0, -22789095, -40428144379]  26542080
227430.x2 227430fy1 [1, -1, 0, -3684975, 1872198125]  13271040 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 227430.x have rank $$1$$.

## Modular form 227430.2.a.x

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 2q^{11} + 4q^{13} - q^{14} + q^{16} + 4q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 