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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 11550.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11550.bs1 | 11550bt2 | \([1, 1, 1, -11305888, 14419449281]\) | \(10228636028672744397625/167006381634183168\) | \(2609474713034112000000\) | \([2]\) | \(1198080\) | \(2.9087\) | |
11550.bs2 | 11550bt1 | \([1, 1, 1, -41888, 632313281]\) | \(-520203426765625/11054534935707648\) | \(-172727108370432000000\) | \([2]\) | \(599040\) | \(2.5621\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11550.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 11550.bs do not have complex multiplication.Modular form 11550.2.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 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.