Properties

Label 1960b
Number of curves $4$
Conductor $1960$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1960b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1960.g3 1960b1 \([0, 0, 0, -98, -343]\) \(55296/5\) \(9411920\) \([2]\) \(288\) \(0.077594\) \(\Gamma_0(N)\)-optimal
1960.g2 1960b2 \([0, 0, 0, -343, 2058]\) \(148176/25\) \(752953600\) \([2, 2]\) \(576\) \(0.42417\)  
1960.g1 1960b3 \([0, 0, 0, -5243, 146118]\) \(132304644/5\) \(602362880\) \([2]\) \(1152\) \(0.77074\)  
1960.g4 1960b4 \([0, 0, 0, 637, 11662]\) \(237276/625\) \(-75295360000\) \([2]\) \(1152\) \(0.77074\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 1960b do not have complex multiplication.

Modular form 1960.2.a.b

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