Properties

Label 1764.g
Number of curves 4
Conductor 1764
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1764.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1764.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1764.g1 1764f4 [0, 0, 0, -806295, -278668978] [2] 13824  
1764.g2 1764f3 [0, 0, 0, -49980, -4429159] [2] 6912  
1764.g3 1764f2 [0, 0, 0, -12495, -172186] [2] 4608  
1764.g4 1764f1 [0, 0, 0, 2940, -20923] [2] 2304 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1764.g have rank \(0\).

Modular form 1764.2.a.g

sage: E.q_eigenform(10)
 
\( q + 6q^{11} - 2q^{13} + 4q^{19} + O(q^{20}) \)

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.