# Properties

 Label 290145.f Number of curves 2 Conductor 290145 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("290145.f1")

sage: E.isogeny_class()

## Elliptic curves in class 290145.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
290145.f1 290145f1 [1, 1, 1, -314131, 67630928]  1451520 $$\Gamma_0(N)$$-optimal
290145.f2 290145f2 [1, 1, 1, -293106, 77100588]  2903040

## Rank

sage: E.rank()

The elliptic curves in class 290145.f have rank $$1$$.

## Modular form 290145.2.a.f

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + 3q^{8} + q^{9} + q^{10} - 2q^{11} + q^{12} + 2q^{13} + q^{15} - q^{16} + 4q^{17} - q^{18} + O(q^{20})$$

## 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. 