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SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 241200.em
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
241200.em1 | 241200em2 | \([0, 0, 0, -10804800, -15099122000]\) | \(-2989967081734144/380653171875\) | \(-17759754387000000000000\) | \([]\) | \(19906560\) | \(3.0031\) | |
241200.em2 | 241200em1 | \([0, 0, 0, 859200, 46582000]\) | \(1503484706816/890163675\) | \(-41531476420800000000\) | \([]\) | \(6635520\) | \(2.4538\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 241200.em have rank \(0\).
Complex multiplication
The elliptic curves in class 241200.em do not have complex multiplication.Modular form 241200.2.a.em
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.