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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 47600bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47600.bq2 | 47600bb1 | \([0, -1, 0, 12592, 101312]\) | \(3449795831/2071552\) | \(-132579328000000\) | \([2]\) | \(153600\) | \(1.3991\) | \(\Gamma_0(N)\)-optimal |
47600.bq1 | 47600bb2 | \([0, -1, 0, -51408, 869312]\) | \(234770924809/130960928\) | \(8381499392000000\) | \([2]\) | \(307200\) | \(1.7457\) |
Rank
sage: E.rank()
The elliptic curves in class 47600bb have rank \(0\).
Complex multiplication
The elliptic curves in class 47600bb do not have complex multiplication.Modular form 47600.2.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 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.