Properties

Label 28900.b
Number of curves 4
Conductor 28900
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("28900.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28900.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28900.b1 28900d3 [0, 1, 0, -298633, -62899512] [2] 165888  
28900.b2 28900d4 [0, 1, 0, -262508, -78650012] [2] 331776  
28900.b3 28900d1 [0, 1, 0, -9633, 246988] [2] 55296 \(\Gamma_0(N)\)-optimal
28900.b4 28900d2 [0, 1, 0, 26492, 1691988] [2] 110592  

Rank

sage: E.rank()
 

The elliptic curves in class 28900.b have rank \(0\).

Modular form 28900.2.a.b

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + 2q^{7} + q^{9} - 2q^{13} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.