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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 75900.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75900.bb1 | 75900ba2 | \([0, 1, 0, -255508, -49534012]\) | \(461188987116496/2811467307\) | \(11245869228000000\) | \([2]\) | \(460800\) | \(1.9187\) | |
75900.bb2 | 75900ba1 | \([0, 1, 0, -255133, -49687012]\) | \(7346581704933376/275517\) | \(68879250000\) | \([2]\) | \(230400\) | \(1.5721\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 75900.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 75900.bb do not have complex multiplication.Modular form 75900.2.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.