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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 3600bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3600.bc3 | 3600bi1 | \([0, 0, 0, -435, 4210]\) | \(-121945/32\) | \(-2388787200\) | \([]\) | \(1440\) | \(0.51635\) | \(\Gamma_0(N)\)-optimal |
3600.bc4 | 3600bi2 | \([0, 0, 0, 3165, -31070]\) | \(46969655/32768\) | \(-2446118092800\) | \([]\) | \(4320\) | \(1.0657\) | |
3600.bc2 | 3600bi3 | \([0, 0, 0, -1875, -368750]\) | \(-25/2\) | \(-58320000000000\) | \([]\) | \(7200\) | \(1.3211\) | |
3600.bc1 | 3600bi4 | \([0, 0, 0, -451875, -116918750]\) | \(-349938025/8\) | \(-233280000000000\) | \([]\) | \(21600\) | \(1.8704\) |
Rank
sage: E.rank()
The elliptic curves in class 3600bi have rank \(1\).
Complex multiplication
The elliptic curves in class 3600bi do not have complex multiplication.Modular form 3600.2.a.bi
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.