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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 162450bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162450.et2 | 162450bs1 | \([1, -1, 1, -191976980, -51824345353]\) | \(212883113611/122880000\) | \(451659516827310720000000000\) | \([2]\) | \(112066560\) | \(3.8041\) | \(\Gamma_0(N)\)-optimal |
162450.et1 | 162450bs2 | \([1, -1, 1, -2167368980, -38737901273353]\) | \(306331959547531/900000000\) | \(3308053101762529687500000000\) | \([2]\) | \(224133120\) | \(4.1507\) |
Rank
sage: E.rank()
The elliptic curves in class 162450bs have rank \(1\).
Complex multiplication
The elliptic curves in class 162450bs do not have complex multiplication.Modular form 162450.2.a.bs
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 Cremona 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 Cremona labels.