Properties

Label 4800.bk
Number of curves $2$
Conductor $4800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 4800.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.bk1 4800cs1 \([0, 1, 0, -1333, -18037]\) \(131072/9\) \(18000000000\) \([2]\) \(3840\) \(0.71604\) \(\Gamma_0(N)\)-optimal
4800.bk2 4800cs2 \([0, 1, 0, 1167, -75537]\) \(5488/81\) \(-2592000000000\) \([2]\) \(7680\) \(1.0626\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4800.bk have rank \(0\).

Complex multiplication

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

Modular form 4800.2.a.bk

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