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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 424830.ej
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.ej1 | 424830ej2 | \([1, 0, 1, -221958798, 1272771222328]\) | \(-12242088317612041/600\) | \(-59270220673200600\) | \([]\) | \(49968576\) | \(3.1421\) | \(\Gamma_0(N)\)-optimal* |
424830.ej2 | 424830ej1 | \([1, 0, 1, -2716173, 1777876678]\) | \(-22434194041/843750\) | \(-83348747821688343750\) | \([]\) | \(16656192\) | \(2.5928\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830.ej have rank \(0\).
Complex multiplication
The elliptic curves in class 424830.ej do not have complex multiplication.Modular form 424830.2.a.ej
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.