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Properties

Label 5010.h
Number of curves $2$
Conductor $5010$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 5010.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5010.h1 5010h2 \([1, 0, 0, -380530, -91764010]\) \(-6093832136609347161121/108676727597808690\) \(-108676727597808690\) \([]\) \(65856\) \(2.0657\)  
5010.h2 5010h1 \([1, 0, 0, -1480, 94400]\) \(-358531401121921/3652290000000\) \(-3652290000000\) \([7]\) \(9408\) \(1.0927\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5010.h have rank \(0\).

Complex multiplication

The elliptic curves in class 5010.h do not have complex multiplication.

Modular form 5010.2.a.h

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.