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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 397800.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
397800.bu1 | 397800bu2 | \([0, 0, 0, -73875, -7177250]\) | \(3822686500/304317\) | \(3549553488000000\) | \([2]\) | \(2359296\) | \(1.7273\) | |
397800.bu2 | 397800bu1 | \([0, 0, 0, -15375, 603250]\) | \(137842000/25857\) | \(75399012000000\) | \([2]\) | \(1179648\) | \(1.3807\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 397800.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 397800.bu do not have complex multiplication.Modular form 397800.2.a.bu
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.