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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 33600br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33600.m2 | 33600br1 | \([0, -1, 0, 667, -15963]\) | \(16384/63\) | \(-126000000000\) | \([2]\) | \(30720\) | \(0.81273\) | \(\Gamma_0(N)\)-optimal |
33600.m1 | 33600br2 | \([0, -1, 0, -6833, -188463]\) | \(1102736/147\) | \(4704000000000\) | \([2]\) | \(61440\) | \(1.1593\) |
Rank
sage: E.rank()
The elliptic curves in class 33600br have rank \(0\).
Complex multiplication
The elliptic curves in class 33600br do not have complex multiplication.Modular form 33600.2.a.br
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.