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Properties

Label 4650.bs
Number of curves $2$
Conductor $4650$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 4650.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4650.bs1 4650bs2 \([1, 0, 0, -5119638, -4459095108]\) \(7598212583918732621/36771465672\) \(71819268890625000\) \([2]\) \(188160\) \(2.4350\)  
4650.bs2 4650bs1 \([1, 0, 0, -314638, -72130108]\) \(-1763710408147661/129263387328\) \(-252467553375000000\) \([2]\) \(94080\) \(2.0884\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4650.bs have rank \(0\).

Complex multiplication

The elliptic curves in class 4650.bs do not have complex multiplication.

Modular form 4650.2.a.bs

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.