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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 213444.eg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
213444.eg1 | 213444ei2 | \([0, 0, 0, -35378343, -69397581330]\) | \(4662947952/717409\) | \(753429168284286366690048\) | \([2]\) | \(33177600\) | \(3.3051\) | |
213444.eg2 | 213444ei1 | \([0, 0, 0, 3841992, -5978299635]\) | \(95551488/290521\) | \(-19069229982401876016432\) | \([2]\) | \(16588800\) | \(2.9585\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 213444.eg have rank \(0\).
Complex multiplication
The elliptic curves in class 213444.eg do not have complex multiplication.Modular form 213444.2.a.eg
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.