Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("1650.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1650.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1650.m1 1650m3 [1, 1, 1, -2013, -35469] [2] 1728  
1650.m2 1650m4 [1, 1, 1, -1013, -69469] [2] 3456  
1650.m3 1650m1 [1, 1, 1, -138, 531] [2] 576 \(\Gamma_0(N)\)-optimal
1650.m4 1650m2 [1, 1, 1, 112, 2531] [2] 1152  

Rank

sage: E.rank()
 

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

Modular form 1650.2.a.m

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.