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SageMath
sage: E = EllipticCurve("15246.m1")
sage: E.isogeny_class()
Elliptic curves in class 15246.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 15246.m1 | 15246i6 | [1, -1, 0, -2973537, -1972852227] | [2] | 207360 | |
| 15246.m2 | 15246i5 | [1, -1, 0, -185697, -30842883] | [2] | 103680 | |
| 15246.m3 | 15246i4 | [1, -1, 0, -38682, -2390580] | [2] | 69120 | |
| 15246.m4 | 15246i2 | [1, -1, 0, -11457, 474579] | [2] | 23040 | |
| 15246.m5 | 15246i1 | [1, -1, 0, -567, 10665] | [2] | 11520 | \(\Gamma_0(N)\)-optimal |
| 15246.m6 | 15246i3 | [1, -1, 0, 4878, -221292] | [2] | 34560 |
Rank
sage: E.rank()
The elliptic curves in class 15246.m have rank \(1\).
Modular form 15246.2.a.m
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
