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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)
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.