Properties

Label 4800.bn
Number of curves $2$
Conductor $4800$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4800.bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.bn1 4800bg1 \([0, 1, 0, -53, 123]\) \(131072/9\) \(1152000\) \([2]\) \(768\) \(-0.088679\) \(\Gamma_0(N)\)-optimal
4800.bn2 4800bg2 \([0, 1, 0, 47, 623]\) \(5488/81\) \(-165888000\) \([2]\) \(1536\) \(0.25789\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4800.bn have rank \(1\).

Complex multiplication

The elliptic curves in class 4800.bn do not have complex multiplication.

Modular form 4800.2.a.bn

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4q^{7} + q^{9} + 4q^{11} - 4q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.