# Properties

 Label 227430.ec Number of curves $6$ Conductor $227430$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("227430.ec1")

sage: E.isogeny_class()

## Elliptic curves in class 227430.ec

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.ec1 227430be6 [1, -1, 1, -54583268, -155202684343] [2] 14155776
227430.ec2 227430be4 [1, -1, 1, -3411518, -2424307543] [2, 2] 7077888
227430.ec3 227430be5 [1, -1, 1, -3184088, -2761631719] [2] 14155776
227430.ec4 227430be3 [1, -1, 1, -1202198, 479830601] [2] 7077888
227430.ec5 227430be2 [1, -1, 1, -227498, -32471719] [2, 2] 3538944
227430.ec6 227430be1 [1, -1, 1, 32422, -3152743] [2] 1769472 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 227430.2.a.ec

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.