# Properties

 Label 227430gg Number of curves $2$ Conductor $227430$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("227430.o1")

sage: E.isogeny_class()

## Elliptic curves in class 227430gg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.o1 227430gg1 [1, -1, 0, -16648485, 26093960981] [2] 22014720 $$\Gamma_0(N)$$-optimal
227430.o2 227430gg2 [1, -1, 0, -10410405, 45879903125] [2] 44029440

## Rank

sage: E.rank()

The elliptic curves in class 227430gg have rank $$0$$.

## Modular form 227430.2.a.o

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + 4q^{11} - 6q^{13} + q^{14} + q^{16} - 4q^{17} + O(q^{20})$$

## 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 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.