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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 161700.ej
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
161700.ej1 | 161700bb2 | \([0, 1, 0, -23508, 527988]\) | \(1047213232/515625\) | \(707437500000000\) | \([2]\) | \(552960\) | \(1.5426\) | |
161700.ej2 | 161700bb1 | \([0, 1, 0, 5367, 65988]\) | \(199344128/136125\) | \(-11672718750000\) | \([2]\) | \(276480\) | \(1.1960\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 161700.ej have rank \(1\).
Complex multiplication
The elliptic curves in class 161700.ej do not have complex multiplication.Modular form 161700.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.