Show commands:
SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 337590.cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 337590.cb1 | 337590cb3 | \([1, -1, 0, -7218459, 7466415853]\) | \(32208729120020809/658986840\) | \(851060395852527960\) | \([2]\) | \(11796480\) | \(2.5600\) | |
| 337590.cb2 | 337590cb2 | \([1, -1, 0, -466659, 108304213]\) | \(8702409880009/1120910400\) | \(1447619877718977600\) | \([2, 2]\) | \(5898240\) | \(2.2134\) | |
| 337590.cb3 | 337590cb1 | \([1, -1, 0, -118179, -13872875]\) | \(141339344329/17141760\) | \(22138033972285440\) | \([2]\) | \(2949120\) | \(1.8668\) | \(\Gamma_0(N)\)-optimal |
| 337590.cb4 | 337590cb4 | \([1, -1, 0, 709461, 565344445]\) | \(30579142915511/124675335000\) | \(-161014201676844615000\) | \([2]\) | \(11796480\) | \(2.5600\) |
Rank
sage: E.rank()
The elliptic curves in class 337590.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 337590.cb do not have complex multiplication.Modular form 337590.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
