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Properties

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

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 4650bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4650.bl2 4650bn1 \([1, 0, 0, 55937, 22542617]\) \(1238798620042199/14760960000000\) \(-230640000000000000\) \([2]\) \(64512\) \(2.0125\) \(\Gamma_0(N)\)-optimal
4650.bl1 4650bn2 \([1, 0, 0, -936063, 325102617]\) \(5805223604235668521/435937500000000\) \(6811523437500000000\) \([2]\) \(129024\) \(2.3591\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4650.2.a.bn

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