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SageMath
E = EllipticCurve("cg1")
E.isogeny_class()
Elliptic curves in class 358160.cg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 358160.cg1 | 358160cg3 | \([0, -1, 0, -10212440, -12558119440]\) | \(16232905099479601/4052240\) | \(29404325259837440\) | \([2]\) | \(9953280\) | \(2.5356\) | |
| 358160.cg2 | 358160cg4 | \([0, -1, 0, -10173720, -12658109968]\) | \(-16048965315233521/256572640900\) | \(-1861771609233182310400\) | \([2]\) | \(19906560\) | \(2.8822\) | |
| 358160.cg3 | 358160cg1 | \([0, -1, 0, -145240, -11600400]\) | \(46694890801/18944000\) | \(137463609688064000\) | \([2]\) | \(3317760\) | \(1.9863\) | \(\Gamma_0(N)\)-optimal |
| 358160.cg4 | 358160cg2 | \([0, -1, 0, 474280, -84951568]\) | \(1625964918479/1369000000\) | \(-9933893668864000000\) | \([2]\) | \(6635520\) | \(2.3329\) |
Rank
sage: E.rank()
The elliptic curves in class 358160.cg have rank \(1\).
Complex multiplication
The elliptic curves in class 358160.cg do not have complex multiplication.Modular form 358160.2.a.cg
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.
