# Properties

 Label 1650.q Number of curves 2 Conductor 1650 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1650.q1")
sage: E.isogeny_class()

## Elliptic curves in class 1650.q

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1650.q1 1650r1 [1, 0, 0, -578, 5412] 5 1200 $$\Gamma_0(N)$$-optimal
1650.q2 1650r2 [1, 0, 0, 3112, -246858] 1 6000

## Rank

sage: E.rank()

The elliptic curves in class 1650.q have rank $$0$$.

## Modular form1650.2.a.q

sage: E.q_eigenform(10)
$$q + q^{2} + q^{3} + q^{4} + q^{6} - 2q^{7} + q^{8} + q^{9} + q^{11} + q^{12} - q^{13} - 2q^{14} + q^{16} + 8q^{17} + q^{18} - 5q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.