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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 9600.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9600.br1 | 9600x1 | \([0, 1, 0, -958, -11662]\) | \(389344/3\) | \(750000000\) | \([2]\) | \(3840\) | \(0.53201\) | \(\Gamma_0(N)\)-optimal |
9600.br2 | 9600x2 | \([0, 1, 0, -333, -26037]\) | \(-128/9\) | \(-288000000000\) | \([2]\) | \(7680\) | \(0.87858\) |
Rank
sage: E.rank()
The elliptic curves in class 9600.br have rank \(1\).
Complex multiplication
The elliptic curves in class 9600.br do not have complex multiplication.Modular form 9600.2.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 LMFDB 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 LMFDB labels.