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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 468270q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 468270.q2 | 468270q1 | \([1, -1, 0, -2745, -33379]\) | \(47832147/17200\) | \(822712928400\) | \([2]\) | \(737280\) | \(0.98707\) | \(\Gamma_0(N)\)-optimal |
| 468270.q1 | 468270q2 | \([1, -1, 0, -39045, -2959159]\) | \(137627865747/36980\) | \(1768832796060\) | \([2]\) | \(1474560\) | \(1.3336\) |
Rank
sage: E.rank()
The elliptic curves in class 468270q have rank \(0\).
Complex multiplication
The elliptic curves in class 468270q do not have complex multiplication.Modular form 468270.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
