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SageMath
E = EllipticCurve("gl1")
E.isogeny_class()
Elliptic curves in class 193200.gl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193200.gl1 | 193200be2 | \([0, 1, 0, -10808, 1970388]\) | \(-2181825073/25039686\) | \(-1602539904000000\) | \([]\) | \(933120\) | \(1.5995\) | |
193200.gl2 | 193200be1 | \([0, 1, 0, 1192, -69612]\) | \(2924207/34776\) | \(-2225664000000\) | \([]\) | \(311040\) | \(1.0502\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193200.gl have rank \(0\).
Complex multiplication
The elliptic curves in class 193200.gl do not have complex multiplication.Modular form 193200.2.a.gl
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.