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SageMath
E = EllipticCurve("ei1")
E.isogeny_class()
Elliptic curves in class 273600.ei
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.ei1 | 273600ei2 | \([0, 0, 0, -432300, -107678000]\) | \(2992209121/54150\) | \(161691033600000000\) | \([2]\) | \(3538944\) | \(2.0973\) | |
273600.ei2 | 273600ei1 | \([0, 0, 0, -300, -4862000]\) | \(-1/3420\) | \(-10212065280000000\) | \([2]\) | \(1769472\) | \(1.7507\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273600.ei have rank \(0\).
Complex multiplication
The elliptic curves in class 273600.ei do not have complex multiplication.Modular form 273600.2.a.ei
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.