# Properties

 Label 227430fp Number of curves $4$ Conductor $227430$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("227430.cu1")

sage: E.isogeny_class()

## Elliptic curves in class 227430fp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.cu3 227430fp1 [1, -1, 0, -16854, -733772] [2] 684288 $$\Gamma_0(N)$$-optimal
227430.cu4 227430fp2 [1, -1, 0, 26466, -3913460] [2] 1368576
227430.cu1 227430fp3 [1, -1, 0, -341754, 76888448] [2] 2052864
227430.cu2 227430fp4 [1, -1, 0, -244284, 121588190] [2] 4105728

## Rank

sage: E.rank()

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

## Modular form 227430.2.a.cu

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.