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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 32490.cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32490.cb1 | 32490bf4 | \([1, -1, 1, -414857, 102949489]\) | \(8527173507/200\) | \(185200815144600\) | \([2]\) | \(331776\) | \(1.8497\) | |
| 32490.cb2 | 32490bf3 | \([1, -1, 1, -24977, 1736641]\) | \(-1860867/320\) | \(-296321304231360\) | \([2]\) | \(165888\) | \(1.5032\) | |
| 32490.cb3 | 32490bf2 | \([1, -1, 1, -8732, -79911]\) | \(57960603/31250\) | \(39694962093750\) | \([2]\) | \(110592\) | \(1.3004\) | |
| 32490.cb4 | 32490bf1 | \([1, -1, 1, 2098, -10599]\) | \(804357/500\) | \(-635119393500\) | \([2]\) | \(55296\) | \(0.95386\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32490.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 32490.cb do not have complex multiplication.Modular form 32490.2.a.cb
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.
