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Properties

Label 118354.s
Number of curves $2$
Conductor $118354$
CM no
Rank $2$
Graph

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

Elliptic curves in class 118354.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
118354.s1 118354s2 \([1, 0, 0, -95464757, 359040207521]\) \(-2281081786314874633/243116158976\) \(-10254769322357872111616\) \([]\) \(17372160\) \(3.2544\)  
118354.s2 118354s1 \([1, 0, 0, 106098, 1491530804]\) \(3131359847/22785865136\) \(-961119950908337040176\) \([]\) \(5790720\) \(2.7051\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 118354.s have rank \(2\).

Complex multiplication

The elliptic curves in class 118354.s do not have complex multiplication.

Modular form 118354.2.a.s

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.