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Properties

Label 10010n
Number of curves $2$
Conductor $10010$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 10010n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10010.r2 10010n1 \([1, -1, 1, 17, -1433]\) \(573856191/881760880\) \(-881760880\) \([2]\) \(4608\) \(0.39543\) \(\Gamma_0(N)\)-optimal
10010.r1 10010n2 \([1, -1, 1, -1803, -28369]\) \(647865799013889/16121205100\) \(16121205100\) \([2]\) \(9216\) \(0.74200\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10010n have rank \(1\).

Complex multiplication

The elliptic curves in class 10010n do not have complex multiplication.

Modular form 10010.2.a.n

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

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.