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SageMath
sage: E = EllipticCurve("g1")
sage: E.isogeny_class()
Elliptic curves in class 6720g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
6720.p3 | 6720g1 | [0, -1, 0, -161, 801] | [2] | 2048 | \(\Gamma_0(N)\)-optimal |
6720.p2 | 6720g2 | [0, -1, 0, -481, -2975] | [2, 2] | 4096 | |
6720.p1 | 6720g3 | [0, -1, 0, -7201, -232799] | [2] | 8192 | |
6720.p4 | 6720g4 | [0, -1, 0, 1119, -19935] | [2] | 8192 |
Rank
sage: E.rank()
The elliptic curves in class 6720g have rank \(0\).
Complex multiplication
The elliptic curves in class 6720g do not have complex multiplication.Modular form 6720.2.a.g
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.