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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 33600bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33600.cb2 | 33600bq1 | \([0, -1, 0, -12293, -868443]\) | \(-1605176213504/1640558367\) | \(-209991470976000\) | \([2]\) | \(129024\) | \(1.4436\) | \(\Gamma_0(N)\)-optimal |
33600.cb1 | 33600bq2 | \([0, -1, 0, -230993, -42640143]\) | \(665567485783184/257298363\) | \(526947047424000\) | \([2]\) | \(258048\) | \(1.7902\) |
Rank
sage: E.rank()
The elliptic curves in class 33600bq have rank \(0\).
Complex multiplication
The elliptic curves in class 33600bq do not have complex multiplication.Modular form 33600.2.a.bq
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.