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SageMath
sage: E = EllipticCurve("42.a1")
sage: E.isogeny_class()
sage: E.isogeny_class()
Elliptic curves in class 42.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion order | Modular degree | Optimality |
---|---|---|---|---|---|
42.a1 | 42a4 | [1, 1, 1, -1344, 18405] | 4 | 16 | |
42.a2 | 42a5 | [1, 1, 1, -914, -10915] | 2 | 32 | |
42.a3 | 42a3 | [1, 1, 1, -104, 101] | 4 | 16 | |
42.a4 | 42a2 | [1, 1, 1, -84, 261] | 8 | 8 | |
42.a5 | 42a1 | [1, 1, 1, -4, 5] | 8 | 4 | \(\Gamma_0(N)\)-optimal |
42.a6 | 42a6 | [1, 1, 1, 386, 1277] | 2 | 32 |
Rank
sage: E.rank()
The elliptic curves in class 42.a have rank \(0\).
Modular form 42.2.1.a
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)