# Properties

 Label 1650.k Number of curves $4$ Conductor $1650$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 1650.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1650.k1 1650f3 [1, 0, 1, -8801, -318502] [2] 2048
1650.k2 1650f2 [1, 0, 1, -551, -5002] [2, 2] 1024
1650.k3 1650f4 [1, 0, 1, -301, -9502] [2] 2048
1650.k4 1650f1 [1, 0, 1, -51, -2] [2] 512 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 1650.k do not have complex multiplication.

## Modular form1650.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} + 4q^{7} - q^{8} + q^{9} - q^{11} + q^{12} + 6q^{13} - 4q^{14} + q^{16} - 2q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.