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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 33150.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33150.bi1 | 33150bl2 | \([1, 1, 1, -1848763, -968312719]\) | \(-71559517896165625/4598568\) | \(-44907890625000\) | \([]\) | \(440640\) | \(2.0785\) | |
33150.bi2 | 33150bl1 | \([1, 1, 1, -20638, -1600219]\) | \(-99546915625/54454842\) | \(-531785566406250\) | \([]\) | \(146880\) | \(1.5292\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33150.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 33150.bi do not have complex multiplication.Modular form 33150.2.a.bi
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.