Properties

Label 882e
Number of curves $6$
Conductor $882$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("882.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 882e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
882.b5 882e1 [1, -1, 0, -1773, 63909] [2] 1536 \(\Gamma_0(N)\)-optimal
882.b4 882e2 [1, -1, 0, -37053, 2752245] [2, 2] 3072  
882.b3 882e3 [1, -1, 0, -45873, 1349865] [2, 2] 6144  
882.b1 882e4 [1, -1, 0, -592713, 175784769] [2] 6144  
882.b2 882e5 [1, -1, 0, -403083, -97454421] [2] 12288  
882.b6 882e6 [1, -1, 0, 170217, 10295991] [2] 12288  

Rank

sage: E.rank()
 

The elliptic curves in class 882e have rank \(1\).

Modular form 882.2.a.b

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.