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SageMath
sage: E = EllipticCurve("n1")
sage: E.isogeny_class()
Elliptic curves in class 17325.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 17325.n1 | 17325s5 | [1, -1, 1, -686070005, 6916900543872] | [2] | 1474560 | |
| 17325.n2 | 17325s4 | [1, -1, 1, -42879380, 108084587622] | [2, 2] | 737280 | |
| 17325.n3 | 17325s6 | [1, -1, 1, -42666755, 109209373872] | [2] | 1474560 | |
| 17325.n4 | 17325s3 | [1, -1, 1, -5725130, -2779063878] | [2] | 737280 | |
| 17325.n5 | 17325s2 | [1, -1, 1, -2693255, 1671728622] | [2, 2] | 368640 | |
| 17325.n6 | 17325s1 | [1, -1, 1, 7870, 78064872] | [2] | 184320 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17325.n have rank \(1\).
Complex multiplication
The elliptic curves in class 17325.n do not have complex multiplication.Modular form 17325.2.a.n
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
