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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 44880.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.cs1 | 44880cu4 | \([0, 1, 0, -9087160, -10546664620]\) | \(20260414982443110947641/720358602480\) | \(2950588835758080\) | \([2]\) | \(884736\) | \(2.4642\) | |
| 44880.cs2 | 44880cu2 | \([0, 1, 0, -568760, -164438700]\) | \(4967657717692586041/29490113030400\) | \(120791502972518400\) | \([2, 2]\) | \(442368\) | \(2.1176\) | |
| 44880.cs3 | 44880cu3 | \([0, 1, 0, -242360, -351531180]\) | \(-384369029857072441/12804787777021680\) | \(-52448410734680801280\) | \([2]\) | \(884736\) | \(2.4642\) | |
| 44880.cs4 | 44880cu1 | \([0, 1, 0, -56760, 834900]\) | \(4937402992298041/2780405760000\) | \(11388541992960000\) | \([2]\) | \(221184\) | \(1.7710\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44880.cs have rank \(1\).
Complex multiplication
The elliptic curves in class 44880.cs do not have complex multiplication.Modular form 44880.2.a.cs
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.
