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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 18480bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18480.m4 | 18480bu1 | \([0, -1, 0, 4104, -136080]\) | \(1865864036231/2993760000\) | \(-12262440960000\) | \([2]\) | \(30720\) | \(1.1966\) | \(\Gamma_0(N)\)-optimal |
18480.m3 | 18480bu2 | \([0, -1, 0, -27896, -1364880]\) | \(586145095611769/140040608400\) | \(573606332006400\) | \([2, 2]\) | \(61440\) | \(1.5432\) | |
18480.m1 | 18480bu3 | \([0, -1, 0, -416696, -103386000]\) | \(1953542217204454969/170843779260\) | \(699776119848960\) | \([2]\) | \(122880\) | \(1.8898\) | |
18480.m2 | 18480bu4 | \([0, -1, 0, -151096, 21501040]\) | \(93137706732176569/5369647977540\) | \(21994078116003840\) | \([2]\) | \(122880\) | \(1.8898\) |
Rank
sage: E.rank()
The elliptic curves in class 18480bu have rank \(1\).
Complex multiplication
The elliptic curves in class 18480bu do not have complex multiplication.Modular form 18480.2.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 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.