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Properties

Label 1650k
Number of curves $2$
Conductor $1650$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 1650k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1650.j2 1650k1 \([1, 0, 1, 22799, 204548]\) \(3355354844375/1987172352\) \(-776239200000000\) \([3]\) \(7920\) \(1.5465\) \(\Gamma_0(N)\)-optimal
1650.j1 1650k2 \([1, 0, 1, -286576, -65259202]\) \(-6663170841705625/850403524608\) \(-332188876800000000\) \([]\) \(23760\) \(2.0958\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1650k have rank \(0\).

Complex multiplication

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

Modular form 1650.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + 2 q^{7} - q^{8} + q^{9} + q^{11} + q^{12} + 5 q^{13} - 2 q^{14} + q^{16} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.