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SageMath
sage: E = EllipticCurve("jq1")
sage: E.isogeny_class()
Elliptic curves in class 277200.jq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 277200.jq1 | 277200jq6 | [0, 0, 0, -10977120075, -442670657687750] | [2] | 94371840 | |
| 277200.jq2 | 277200jq4 | [0, 0, 0, -686070075, -6916727537750] | [2, 2] | 47185920 | |
| 277200.jq3 | 277200jq5 | [0, 0, 0, -682668075, -6988717259750] | [2] | 94371840 | |
| 277200.jq4 | 277200jq3 | [0, 0, 0, -91602075, 177951690250] | [2] | 47185920 | |
| 277200.jq5 | 277200jq2 | [0, 0, 0, -43092075, -106947539750] | [2, 2] | 23592960 | |
| 277200.jq6 | 277200jq1 | [0, 0, 0, 125925, -4996277750] | [2] | 11796480 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.jq have rank \(0\).
Complex multiplication
The elliptic curves in class 277200.jq do not have complex multiplication.Modular form 277200.2.a.jq
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.
