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Properties

Label 116242.s
Number of curves $2$
Conductor $116242$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 116242.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116242.s1 116242w2 \([1, 1, 1, -1249609, 533817999]\) \(4586955865263577/32713753576\) \(1539047357799820456\) \([]\) \(3110400\) \(2.3220\)  
116242.s2 116242w1 \([1, 1, 1, -99824, -11710761]\) \(2338337977417/102825226\) \(4837503346194106\) \([]\) \(1036800\) \(1.7727\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 116242.s have rank \(0\).

Complex multiplication

The elliptic curves in class 116242.s do not have complex multiplication.

Modular form 116242.2.a.s

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.