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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 217800ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 217800.gz4 | 217800ct1 | \([0, 0, 0, 18150, 25788125]\) | \(2048/891\) | \(-287674490094750000\) | \([2]\) | \(2949120\) | \(2.0291\) | \(\Gamma_0(N)\)-optimal |
| 217800.gz3 | 217800ct2 | \([0, 0, 0, -1206975, 497461250]\) | \(37642192/1089\) | \(5625634472964000000\) | \([2, 2]\) | \(5898240\) | \(2.3757\) | |
| 217800.gz1 | 217800ct3 | \([0, 0, 0, -19175475, 32319674750]\) | \(37736227588/33\) | \(681895087632000000\) | \([2]\) | \(11796480\) | \(2.7223\) | |
| 217800.gz2 | 217800ct4 | \([0, 0, 0, -2840475, -1137672250]\) | \(122657188/43923\) | \(907602361638192000000\) | \([2]\) | \(11796480\) | \(2.7223\) |
Rank
sage: E.rank()
The elliptic curves in class 217800ct have rank \(0\).
Complex multiplication
The elliptic curves in class 217800ct do not have complex multiplication.Modular form 217800.2.a.ct
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
