Properties

Label 816.b
Number of curves 6
Conductor 816
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("816.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 816.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
816.b1 816h5 [0, -1, 0, -443904, 113984640] [4] 3072  
816.b2 816h3 [0, -1, 0, -27744, 1787904] [2, 4] 1536  
816.b3 816h6 [0, -1, 0, -26304, 1980288] [4] 3072  
816.b4 816h2 [0, -1, 0, -1824, 25344] [2, 2] 768  
816.b5 816h1 [0, -1, 0, -544, -4352] [2] 384 \(\Gamma_0(N)\)-optimal
816.b6 816h4 [0, -1, 0, 3616, 142848] [2] 1536  

Rank

sage: E.rank()
 

The elliptic curves in class 816.b have rank \(1\).

Modular form 816.2.a.b

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.