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SageMath
E = EllipticCurve("ei1")
E.isogeny_class()
Elliptic curves in class 424830ei
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.ei1 | 424830ei1 | \([1, 0, 1, -1626728, -820502602]\) | \(-5831629329001/186624000\) | \(-15235114991249664000\) | \([]\) | \(16166304\) | \(2.4567\) | \(\Gamma_0(N)\)-optimal* |
424830.ei2 | 424830ei2 | \([1, 0, 1, 7557097, -3017273542]\) | \(584669638645799/386547056640\) | \(-31555903085559718871040\) | \([]\) | \(48498912\) | \(3.0060\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830ei have rank \(0\).
Complex multiplication
The elliptic curves in class 424830ei do not have complex multiplication.Modular form 424830.2.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 Cremona 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 Cremona labels.