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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 259182.fu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259182.fu1 | 259182fu3 | \([1, -1, 1, -5531054, 5008177221]\) | \(14489843500598257/6246072\) | \(8066601920067768\) | \([2]\) | \(8847360\) | \(2.3948\) | |
| 259182.fu2 | 259182fu4 | \([1, -1, 1, -739454, -129184635]\) | \(34623662831857/14438442312\) | \(18646785768202304328\) | \([2]\) | \(8847360\) | \(2.3948\) | |
| 259182.fu3 | 259182fu2 | \([1, -1, 1, -347414, 77498853]\) | \(3590714269297/73410624\) | \(94807469480302656\) | \([2, 2]\) | \(4423680\) | \(2.0482\) | |
| 259182.fu4 | 259182fu1 | \([1, -1, 1, 1066, 3621093]\) | \(103823/4386816\) | \(-5665432349896704\) | \([2]\) | \(2211840\) | \(1.7017\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259182.fu have rank \(0\).
Complex multiplication
The elliptic curves in class 259182.fu do not have complex multiplication.Modular form 259182.2.a.fu
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
