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SageMath
sage: E = EllipticCurve("k1")
sage: E.isogeny_class()
Elliptic curves in class 79350.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 79350.k1 | 79350e4 | [1, 1, 0, -1460040275, -21473739057375] | [2] | 19464192 | |
| 79350.k2 | 79350e6 | [1, 1, 0, -341602025, 2081475474375] | [2] | 38928384 | |
| 79350.k3 | 79350e3 | [1, 1, 0, -93633275, -317126244375] | [2, 2] | 19464192 | |
| 79350.k4 | 79350e2 | [1, 1, 0, -91252775, -335553694875] | [2, 2] | 9732096 | |
| 79350.k5 | 79350e1 | [1, 1, 0, -5554775, -5530696875] | [2] | 4866048 | \(\Gamma_0(N)\)-optimal |
| 79350.k6 | 79350e5 | [1, 1, 0, 116247475, -1536323521125] | [2] | 38928384 |
Rank
sage: E.rank()
The elliptic curves in class 79350.k have rank \(0\).
Complex multiplication
The elliptic curves in class 79350.k do not have complex multiplication.Modular form 79350.2.a.k
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
