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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 122304.ej
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 122304.ej1 | 122304bn1 | \([0, -1, 0, -127661, -16451427]\) | \(1909913257984/129730653\) | \(15628985953072128\) | \([2]\) | \(1474560\) | \(1.8559\) | \(\Gamma_0(N)\)-optimal |
| 122304.ej2 | 122304bn2 | \([0, -1, 0, 110479, -70985487]\) | \(77366117936/1172914587\) | \(-2260864667581857792\) | \([2]\) | \(2949120\) | \(2.2025\) |
Rank
sage: E.rank()
The elliptic curves in class 122304.ej have rank \(0\).
Complex multiplication
The elliptic curves in class 122304.ej do not have complex multiplication.Modular form 122304.2.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.
