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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 493680bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.bb4 | 493680bb1 | \([0, -1, 0, 7704, -30864]\) | \(6967871/4080\) | \(-29605760532480\) | \([2]\) | \(983040\) | \(1.2743\) | \(\Gamma_0(N)\)-optimal* |
493680.bb3 | 493680bb2 | \([0, -1, 0, -31016, -216720]\) | \(454756609/260100\) | \(1887367233945600\) | \([2, 2]\) | \(1966080\) | \(1.6209\) | \(\Gamma_0(N)\)-optimal* |
493680.bb2 | 493680bb3 | \([0, -1, 0, -321416, 69943920]\) | \(506071034209/2505630\) | \(18181637687009280\) | \([2]\) | \(3932160\) | \(1.9675\) | \(\Gamma_0(N)\)-optimal* |
493680.bb1 | 493680bb4 | \([0, -1, 0, -360136, -82891664]\) | \(711882749089/1721250\) | \(12489930224640000\) | \([2]\) | \(3932160\) | \(1.9675\) |
Rank
sage: E.rank()
The elliptic curves in class 493680bb have rank \(1\).
Complex multiplication
The elliptic curves in class 493680bb do not have complex multiplication.Modular form 493680.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.