# Properties

 Label 227430ge Number of curves $2$ Conductor $227430$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("227430.g1")

sage: E.isogeny_class()

## Elliptic curves in class 227430ge

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.g2 227430ge1 [1, -1, 0, -8190, 1061120]  829440 $$\Gamma_0(N)$$-optimal
227430.g1 227430ge2 [1, -1, 0, -213960, 38058566]  1658880

## Rank

sage: E.rank()

The elliptic curves in class 227430ge have rank $$2$$.

## Modular form 227430.2.a.g

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 