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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 262080o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 262080.o3 | 262080o1 | \([0, 0, 0, -11703, 450452]\) | \(3799337068864/319921875\) | \(14926275000000\) | \([2]\) | \(524288\) | \(1.2696\) | \(\Gamma_0(N)\)-optimal |
| 262080.o2 | 262080o2 | \([0, 0, 0, -39828, -2542048]\) | \(2339923888576/419225625\) | \(1251801008640000\) | \([2, 2]\) | \(1048576\) | \(1.6161\) | |
| 262080.o4 | 262080o3 | \([0, 0, 0, 77172, -14663248]\) | \(2127774087928/5119712325\) | \(-122299032696422400\) | \([2]\) | \(2097152\) | \(1.9627\) | |
| 262080.o1 | 262080o4 | \([0, 0, 0, -606828, -181940848]\) | \(1034529986960072/44983575\) | \(1074561881702400\) | \([2]\) | \(2097152\) | \(1.9627\) |
Rank
sage: E.rank()
The elliptic curves in class 262080o have rank \(1\).
Complex multiplication
The elliptic curves in class 262080o do not have complex multiplication.Modular form 262080.2.a.o
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 Cremona 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 Cremona labels.
