# Properties

 Label 33150v Number of curves 2 Conductor 33150 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33150.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 33150v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33150.ba1 33150v1 [1, 0, 1, -340501, 75575648]  368640 $$\Gamma_0(N)$$-optimal
33150.ba2 33150v2 [1, 0, 1, -52501, 199415648]  737280

## Rank

sage: E.rank()

The elliptic curves in class 33150v have rank $$0$$.

## Modular form 33150.2.a.ba

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{12} + q^{13} - 2q^{14} + q^{16} + q^{17} - q^{18} + 2q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 