Properties

Label 100010c
Number of curves 2
Conductor 100010
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("100010.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100010c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100010.c1 100010c1 [1, 1, 0, -5203, -146643] [2] 102400 \(\Gamma_0(N)\)-optimal
100010.c2 100010c2 [1, 1, 0, -5123, -151267] [2] 204800  

Rank

sage: E.rank()
 

The elliptic curves in class 100010c have rank \(1\).

Modular form 100010.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} + 2q^{3} + q^{4} - q^{5} - 2q^{6} - 2q^{7} - q^{8} + q^{9} + q^{10} - 2q^{11} + 2q^{12} - 2q^{13} + 2q^{14} - 2q^{15} + q^{16} - 6q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.