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Properties

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

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 62790.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62790.c1 62790c4 \([1, 1, 0, -223268, -40698948]\) \(1230853025797494103369/22246120260\) \(22246120260\) \([2]\) \(344064\) \(1.5238\)  
62790.c2 62790c3 \([1, 1, 0, -20988, 61668]\) \(1022513876130139849/589590706477500\) \(589590706477500\) \([2]\) \(344064\) \(1.5238\)  
62790.c3 62790c2 \([1, 1, 0, -13968, -638928]\) \(301422017050140169/1277397248400\) \(1277397248400\) \([2, 2]\) \(172032\) \(1.1772\)  
62790.c4 62790c1 \([1, 1, 0, -448, -19712]\) \(-9978645018889/158917973760\) \(-158917973760\) \([2]\) \(86016\) \(0.83061\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 62790.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.