Properties

Label 1650.g
Number of curves $2$
Conductor $1650$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 1650.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1650.g1 1650j2 \([1, 0, 1, -3051, -133802]\) \(-5023028944825/9420668928\) \(-5887918080000\) \([]\) \(3888\) \(1.1402\)  
1650.g2 1650j1 \([1, 0, 1, 324, 3898]\) \(6045109175/13856832\) \(-8660520000\) \([3]\) \(1296\) \(0.59090\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1650.g have rank \(1\).

Complex multiplication

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

Modular form 1650.2.a.g

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