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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 5610.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5610.g1 | 5610f3 | \([1, 1, 0, -567947, 164507661]\) | \(20260414982443110947641/720358602480\) | \(720358602480\) | \([2]\) | \(36864\) | \(1.7710\) | |
| 5610.g2 | 5610f2 | \([1, 1, 0, -35547, 2551581]\) | \(4967657717692586041/29490113030400\) | \(29490113030400\) | \([2, 2]\) | \(18432\) | \(1.4245\) | |
| 5610.g3 | 5610f4 | \([1, 1, 0, -15147, 5485101]\) | \(-384369029857072441/12804787777021680\) | \(-12804787777021680\) | \([2]\) | \(36864\) | \(1.7710\) | |
| 5610.g4 | 5610f1 | \([1, 1, 0, -3547, -14819]\) | \(4937402992298041/2780405760000\) | \(2780405760000\) | \([2]\) | \(9216\) | \(1.0779\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5610.g have rank \(0\).
Complex multiplication
The elliptic curves in class 5610.g do not have complex multiplication.Modular form 5610.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
