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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 32674.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32674.d1 | 32674d4 | \([1, 1, 1, -108613, 9475417]\) | \(159661140625/48275138\) | \(42844362675782978\) | \([2]\) | \(362880\) | \(1.8965\) | |
| 32674.d2 | 32674d3 | \([1, 1, 1, -99003, 11947109]\) | \(120920208625/19652\) | \(17441222339012\) | \([2]\) | \(181440\) | \(1.5499\) | |
| 32674.d3 | 32674d2 | \([1, 1, 1, -41343, -3252067]\) | \(8805624625/2312\) | \(2051908510472\) | \([2]\) | \(120960\) | \(1.3472\) | |
| 32674.d4 | 32674d1 | \([1, 1, 1, -2903, -38483]\) | \(3048625/1088\) | \(965604004928\) | \([2]\) | \(60480\) | \(1.0006\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32674.d have rank \(0\).
Complex multiplication
The elliptic curves in class 32674.d do not have complex multiplication.Modular form 32674.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
