Properties

Label 5082.s
Number of curves $2$
Conductor $5082$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5082.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5082.s1 5082t2 \([1, 1, 1, -12768, 523227]\) \(129938649625/7072758\) \(12529822235238\) \([2]\) \(15360\) \(1.2692\)  
5082.s2 5082t1 \([1, 1, 1, 542, 33419]\) \(9938375/274428\) \(-486165942108\) \([2]\) \(7680\) \(0.92258\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5082.s have rank \(0\).

Complex multiplication

The elliptic curves in class 5082.s do not have complex multiplication.

Modular form 5082.2.a.s

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.