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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 6720bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6720.bs1 | 6720bz1 | \([0, 1, 0, -21, -21]\) | \(1048576/525\) | \(537600\) | \([2]\) | \(768\) | \(-0.20764\) | \(\Gamma_0(N)\)-optimal |
| 6720.bs2 | 6720bz2 | \([0, 1, 0, 79, -81]\) | \(3286064/2205\) | \(-36126720\) | \([2]\) | \(1536\) | \(0.13893\) |
Rank
sage: E.rank()
The elliptic curves in class 6720bz have rank \(0\).
Complex multiplication
The elliptic curves in class 6720bz do not have complex multiplication.Modular form 6720.2.a.bz
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
