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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 19800c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19800.u3 | 19800c1 | \([0, 0, 0, -2775, 54250]\) | \(810448/33\) | \(96228000000\) | \([2]\) | \(16384\) | \(0.87329\) | \(\Gamma_0(N)\)-optimal |
| 19800.u2 | 19800c2 | \([0, 0, 0, -7275, -166250]\) | \(3650692/1089\) | \(12702096000000\) | \([2, 2]\) | \(32768\) | \(1.2199\) | |
| 19800.u1 | 19800c3 | \([0, 0, 0, -106275, -13333250]\) | \(5690357426/891\) | \(20785248000000\) | \([2]\) | \(65536\) | \(1.5664\) | |
| 19800.u4 | 19800c4 | \([0, 0, 0, 19725, -1111250]\) | \(36382894/43923\) | \(-1024635744000000\) | \([2]\) | \(65536\) | \(1.5664\) |
Rank
sage: E.rank()
The elliptic curves in class 19800c have rank \(0\).
Complex multiplication
The elliptic curves in class 19800c do not have complex multiplication.Modular form 19800.2.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 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.
