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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 259920.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.c1 | 259920c4 | \([0, 0, 0, -158032443, -764658453782]\) | \(3107086841064961/570\) | \(80072601321185280\) | \([2]\) | \(26542080\) | \(3.0792\) | |
| 259920.c2 | 259920c3 | \([0, 0, 0, -11437563, -7921335638]\) | \(1177918188481/488703750\) | \(68652246557751229440000\) | \([2]\) | \(26542080\) | \(3.0792\) | |
| 259920.c3 | 259920c2 | \([0, 0, 0, -9878043, -11945209142]\) | \(758800078561/324900\) | \(45641382753075609600\) | \([2, 2]\) | \(13271040\) | \(2.7326\) | |
| 259920.c4 | 259920c1 | \([0, 0, 0, -520923, -246937718]\) | \(-111284641/123120\) | \(-17295681885376020480\) | \([2]\) | \(6635520\) | \(2.3860\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.c have rank \(0\).
Complex multiplication
The elliptic curves in class 259920.c do not have complex multiplication.Modular form 259920.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
