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SageMath
sage: E = EllipticCurve("6930.a1")
sage: E.isogeny_class()
Elliptic curves in class 6930g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 6930.a5 | 6930g1 | [1, -1, 0, 315, -25259] | [2] | 8192 | \(\Gamma_0(N)\)-optimal |
| 6930.a4 | 6930g2 | [1, -1, 0, -11205, -437675] | [2, 2] | 16384 | |
| 6930.a2 | 6930g3 | [1, -1, 0, -177525, -28745339] | [2] | 32768 | |
| 6930.a3 | 6930g4 | [1, -1, 0, -29205, 1337125] | [2, 2] | 32768 | |
| 6930.a1 | 6930g5 | [1, -1, 0, -426105, 107150665] | [2] | 65536 | |
| 6930.a6 | 6930g6 | [1, -1, 0, 79695, 8894785] | [2] | 65536 |
Rank
sage: E.rank()
The elliptic curves in class 6930g have rank \(1\).
Modular form 6930.2.a.a
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
