Properties

Label 28830.bf
Number of curves $6$
Conductor $28830$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("28830.bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28830.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28830.bf1 28830bd6 [1, 1, 1, -295526740, 1955311431257] [2] 3932160  
28830.bf2 28830bd4 [1, 1, 1, -18470440, 30545903897] [2, 2] 1966080  
28830.bf3 28830bd5 [1, 1, 1, -18182140, 31545958937] [2] 3932160  
28830.bf4 28830bd3 [1, 1, 1, -3555720, -2013575655] [2] 1966080  
28830.bf5 28830bd2 [1, 1, 1, -1172440, 461222297] [2, 2] 983040  
28830.bf6 28830bd1 [1, 1, 1, 57640, 30202265] [4] 491520 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28830.bf have rank \(0\).

Modular form 28830.2.a.bf

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} - 6q^{13} - q^{15} + q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.