Properties

Label 62790h
Number of curves $4$
Conductor $62790$
CM no
Rank $1$
Graph

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

Elliptic curves in class 62790h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62790.g3 62790h1 \([1, 1, 0, -532, -4736]\) \(16700655633481/861478800\) \(861478800\) \([2]\) \(36864\) \(0.47221\) \(\Gamma_0(N)\)-optimal
62790.g2 62790h2 \([1, 1, 0, -1512, 16236]\) \(382672988497801/98564602500\) \(98564602500\) \([2, 2]\) \(73728\) \(0.81879\)  
62790.g4 62790h3 \([1, 1, 0, 3738, 109686]\) \(5773777631458199/8392165741050\) \(-8392165741050\) \([2]\) \(147456\) \(1.1654\)  
62790.g1 62790h4 \([1, 1, 0, -22442, 1284594]\) \(1250082349340708521/132447656250\) \(132447656250\) \([2]\) \(147456\) \(1.1654\)  

Rank

sage: E.rank()
 

The elliptic curves in class 62790h have rank \(1\).

Complex multiplication

The elliptic curves in class 62790h do not have complex multiplication.

Modular form 62790.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.