# Properties

 Label 227430.cf Number of curves $4$ Conductor $227430$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cf1")

sage: E.isogeny_class()

## Elliptic curves in class 227430.cf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.cf1 227430em3 [1, -1, 0, -1213569, 514873503]  3686400
227430.cf2 227430em2 [1, -1, 0, -76419, 7932033] [2, 2] 1843200
227430.cf3 227430em1 [1, -1, 0, -11439, -294435]  921600 $$\Gamma_0(N)$$-optimal
227430.cf4 227430em4 [1, -1, 0, 21051, 26704755]  3686400

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 227430.cf do not have complex multiplication.

## Modular form 227430.2.a.cf

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 LMFDB 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 LMFDB labels. 