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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 254100.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254100.bs1 | 254100bs2 | \([0, -1, 0, -7203533, 20447768937]\) | \(-5833703071744/22107421875\) | \(-156658585617187500000000\) | \([]\) | \(22394880\) | \(3.1363\) | |
254100.bs2 | 254100bs1 | \([0, -1, 0, 782467, -667215063]\) | \(7476617216/31444875\) | \(-222826056799500000000\) | \([]\) | \(7464960\) | \(2.5870\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254100.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 254100.bs do not have complex multiplication.Modular form 254100.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.