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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 34650e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
34650.br1 | 34650e1 | \([1, -1, 0, -6567, -203159]\) | \(74246873427/16940\) | \(7146562500\) | \([2]\) | \(49152\) | \(0.88261\) | \(\Gamma_0(N)\)-optimal |
34650.br2 | 34650e2 | \([1, -1, 0, -5817, -251909]\) | \(-51603494067/35870450\) | \(-15132846093750\) | \([2]\) | \(98304\) | \(1.2292\) |
Rank
sage: E.rank()
The elliptic curves in class 34650e have rank \(0\).
Complex multiplication
The elliptic curves in class 34650e do not have complex multiplication.Modular form 34650.2.a.e
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.