Properties

Label 10010.a
Number of curves 4
Conductor 10010
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("10010.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10010.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10010.a1 10010f4 [1, 0, 1, -78985959, -270129426454] [2] 1451520  
10010.a2 10010f3 [1, 0, 1, -5585639, -3040342038] [2] 725760  
10010.a3 10010f2 [1, 0, 1, -2633144, 1164731142] [6] 483840  
10010.a4 10010f1 [1, 0, 1, -2413624, 1442906886] [6] 241920 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10010.a have rank \(0\).

Modular form 10010.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} - 2q^{3} + q^{4} - q^{5} + 2q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + q^{11} - 2q^{12} + q^{13} - q^{14} + 2q^{15} + q^{16} - q^{18} + 2q^{19} + O(q^{20}) \)

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.