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SageMath
E = EllipticCurve("qt1")
E.isogeny_class()
Elliptic curves in class 348480.qt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.qt1 | 348480qt4 | \([0, 0, 0, -30929052, -66206090896]\) | \(154639330142416/33275\) | \(704079407816294400\) | \([2]\) | \(19906560\) | \(2.8093\) | |
| 348480.qt2 | 348480qt3 | \([0, 0, 0, -1939872, -1026818584]\) | \(610462990336/8857805\) | \(11714121147543598080\) | \([2]\) | \(9953280\) | \(2.4627\) | |
| 348480.qt3 | 348480qt2 | \([0, 0, 0, -437052, -62844496]\) | \(436334416/171875\) | \(3636773800704000000\) | \([2]\) | \(6635520\) | \(2.2600\) | |
| 348480.qt4 | 348480qt1 | \([0, 0, 0, -197472, 33083336]\) | \(643956736/15125\) | \(20002255903872000\) | \([2]\) | \(3317760\) | \(1.9134\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 348480.qt have rank \(0\).
Complex multiplication
The elliptic curves in class 348480.qt do not have complex multiplication.Modular form 348480.2.a.qt
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.
