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Properties

Label 28050.bk
Number of curves $2$
Conductor $28050$
CM no
Rank $0$
Graph

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

Elliptic curves in class 28050.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28050.bk1 28050bj1 \([1, 0, 1, -226, -652]\) \(81182737/35904\) \(561000000\) \([2]\) \(12288\) \(0.37448\) \(\Gamma_0(N)\)-optimal
28050.bk2 28050bj2 \([1, 0, 1, 774, -4652]\) \(3288008303/2517768\) \(-39340125000\) \([2]\) \(24576\) \(0.72105\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28050.bk have rank \(0\).

Complex multiplication

The elliptic curves in class 28050.bk do not have complex multiplication.

Modular form 28050.2.a.bk

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