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Properties

Label 4650.bu
Number of curves $2$
Conductor $4650$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 4650.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4650.bu1 4650bp2 \([1, 0, 0, -59388, -8815608]\) \(-2372030262025/2061298872\) \(-20129871796875000\) \([]\) \(36000\) \(1.8258\)  
4650.bu2 4650bp1 \([1, 0, 0, -1428, 62352]\) \(-12882119799145/59982446592\) \(-1499561164800\) \([5]\) \(7200\) \(1.0210\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4650.2.a.bu

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.