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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 15600.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.bi1 | 15600e3 | \([0, -1, 0, -7608, 251712]\) | \(3044193988/85293\) | \(1364688000000\) | \([2]\) | \(32768\) | \(1.1076\) | |
| 15600.bi2 | 15600e2 | \([0, -1, 0, -1108, -8288]\) | \(37642192/13689\) | \(54756000000\) | \([2, 2]\) | \(16384\) | \(0.76098\) | |
| 15600.bi3 | 15600e1 | \([0, -1, 0, -983, -11538]\) | \(420616192/117\) | \(29250000\) | \([2]\) | \(8192\) | \(0.41441\) | \(\Gamma_0(N)\)-optimal |
| 15600.bi4 | 15600e4 | \([0, -1, 0, 3392, -62288]\) | \(269676572/257049\) | \(-4112784000000\) | \([2]\) | \(32768\) | \(1.1076\) |
Rank
sage: E.rank()
The elliptic curves in class 15600.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 15600.bi do not have complex multiplication.Modular form 15600.2.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 LMFDB 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 LMFDB labels.
