# Properties

 Label 227430fi Number of curves $4$ Conductor $227430$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("227430.p1")

sage: E.isogeny_class()

## Elliptic curves in class 227430fi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.p4 227430fi1 [1, -1, 0, -151817715, -848068440075] [2] 77414400 $$\Gamma_0(N)$$-optimal
227430.p3 227430fi2 [1, -1, 0, -2547240435, -49480419586059] [2, 2] 154828800
227430.p2 227430fi3 [1, -1, 0, -2665763955, -44622827937675] [2] 309657600
227430.p1 227430fi4 [1, -1, 0, -40755480435, -3166837229650059] [2] 309657600

## Rank

sage: E.rank()

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

## Modular form 227430.2.a.p

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.