Properties

Label 8550.s
Number of curves $4$
Conductor $8550$
CM no
Rank $0$
Graph

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

Elliptic curves in class 8550.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.s1 8550bh3 \([1, -1, 1, -110808005, -448929368503]\) \(13209596798923694545921/92340\) \(1051810312500\) \([2]\) \(737280\) \(2.8415\)  
8550.s2 8550bh4 \([1, -1, 1, -7011005, -6831098503]\) \(3345930611358906241/165622259047500\) \(1886541044462929687500\) \([2]\) \(737280\) \(2.8415\)  
8550.s3 8550bh2 \([1, -1, 1, -6925505, -7013213503]\) \(3225005357698077121/8526675600\) \(97124164256250000\) \([2, 2]\) \(368640\) \(2.4949\)  
8550.s4 8550bh1 \([1, -1, 1, -427505, -112337503]\) \(-758575480593601/40535043840\) \(-461719483740000000\) \([4]\) \(184320\) \(2.1484\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8550.s have rank \(0\).

Complex multiplication

The elliptic curves in class 8550.s do not have complex multiplication.

Modular form 8550.2.a.s

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