Properties

Label 2960.g
Number of curves $4$
Conductor $2960$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2960.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2960.g1 2960e3 \([0, 0, 0, -6323, 193522]\) \(6825481747209/46250\) \(189440000\) \([2]\) \(1536\) \(0.76966\)  
2960.g2 2960e2 \([0, 0, 0, -403, 2898]\) \(1767172329/136900\) \(560742400\) \([2, 2]\) \(768\) \(0.42308\)  
2960.g3 2960e1 \([0, 0, 0, -83, -238]\) \(15438249/2960\) \(12124160\) \([2]\) \(384\) \(0.076511\) \(\Gamma_0(N)\)-optimal
2960.g4 2960e4 \([0, 0, 0, 397, 12978]\) \(1689410871/18741610\) \(-76765634560\) \([2]\) \(1536\) \(0.76966\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2960.g have rank \(0\).

Complex multiplication

The elliptic curves in class 2960.g do not have complex multiplication.

Modular form 2960.2.a.g

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.