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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 58800.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.be1 | 58800fp1 | \([0, -1, 0, -6008, 70512]\) | \(1092727/540\) | \(11854080000000\) | \([2]\) | \(110592\) | \(1.2017\) | \(\Gamma_0(N)\)-optimal |
58800.be2 | 58800fp2 | \([0, -1, 0, 21992, 518512]\) | \(53582633/36450\) | \(-800150400000000\) | \([2]\) | \(221184\) | \(1.5483\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.be have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.be do not have complex multiplication.Modular form 58800.2.a.be
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.