Properties

Label 1960.g
Number of curves 4
Conductor 1960
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1960.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1960.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1960.g1 1960b3 [0, 0, 0, -5243, 146118] [2] 1152  
1960.g2 1960b2 [0, 0, 0, -343, 2058] [2, 2] 576  
1960.g3 1960b1 [0, 0, 0, -98, -343] [2] 288 \(\Gamma_0(N)\)-optimal
1960.g4 1960b4 [0, 0, 0, 637, 11662] [2] 1152  

Rank

sage: E.rank()
 

The elliptic curves in class 1960.g have rank \(0\).

Modular form 1960.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{5} - 3q^{9} + 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.