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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 393129.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 393129.q1 | 393129q1 | \([1, -1, 1, -5446475, 4429942058]\) | \(1157625/121\) | \(1867616292826060883073\) | \([2]\) | \(19699200\) | \(2.8166\) | \(\Gamma_0(N)\)-optimal |
| 393129.q2 | 393129q2 | \([1, -1, 1, 7002610, 21729190574]\) | \(2460375/14641\) | \(-225981571431953366851833\) | \([2]\) | \(39398400\) | \(3.1631\) |
Rank
sage: E.rank()
The elliptic curves in class 393129.q have rank \(0\).
Complex multiplication
The elliptic curves in class 393129.q do not have complex multiplication.Modular form 393129.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
