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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 92736.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92736.bb1 | 92736bp2 | \([0, 0, 0, -8076, 270160]\) | \(2438569736/91287\) | \(2180652171264\) | \([2]\) | \(114688\) | \(1.1363\) | |
92736.bb2 | 92736bp1 | \([0, 0, 0, 204, 15136]\) | \(314432/33327\) | \(-99513888768\) | \([2]\) | \(57344\) | \(0.78971\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92736.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 92736.bb do not have complex multiplication.Modular form 92736.2.a.bb
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.