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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 7800.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7800.d1 | 7800a3 | \([0, -1, 0, -20808, -1148388]\) | \(62275269892/39\) | \(624000000\) | \([2]\) | \(8192\) | \(1.0078\) | |
| 7800.d2 | 7800a2 | \([0, -1, 0, -1308, -17388]\) | \(61918288/1521\) | \(6084000000\) | \([2, 2]\) | \(4096\) | \(0.66127\) | |
| 7800.d3 | 7800a1 | \([0, -1, 0, -183, 612]\) | \(2725888/1053\) | \(263250000\) | \([2]\) | \(2048\) | \(0.31470\) | \(\Gamma_0(N)\)-optimal |
| 7800.d4 | 7800a4 | \([0, -1, 0, 192, -56388]\) | \(48668/85683\) | \(-1370928000000\) | \([2]\) | \(8192\) | \(1.0078\) |
Rank
sage: E.rank()
The elliptic curves in class 7800.d have rank \(1\).
Complex multiplication
The elliptic curves in class 7800.d do not have complex multiplication.Modular form 7800.2.a.d
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.
