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SageMath
sage: E = EllipticCurve("bj1")
sage: E.isogeny_class()
Elliptic curves in class 6720bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
6720.a3 | 6720bj1 | [0, -1, 0, -36, -30] | [2] | 1536 | \(\Gamma_0(N)\)-optimal |
6720.a2 | 6720bj2 | [0, -1, 0, -281, 1881] | [2, 2] | 3072 | |
6720.a1 | 6720bj3 | [0, -1, 0, -4481, 116961] | [2] | 6144 | |
6720.a4 | 6720bj4 | [0, -1, 0, -1, 5185] | [2] | 6144 |
Rank
sage: E.rank()
The elliptic curves in class 6720bj have rank \(2\).
Complex multiplication
The elliptic curves in class 6720bj do not have complex multiplication.Modular form 6720.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.