# Properties

 Label 147294.cp Number of curves $2$ Conductor $147294$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("147294.cp1")

sage: E.isogeny_class()

## Elliptic curves in class 147294.cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
147294.cp1 147294bg2 [1, -1, 1, -54914, -4925847]  663552
147294.cp2 147294bg1 [1, -1, 1, -1994, -141879]  331776 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 147294.cp have rank $$1$$.

## Modular form 147294.2.a.cp

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2q^{5} + q^{8} + 2q^{10} + 4q^{11} + q^{16} - 4q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 