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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 106930.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106930.w1 | 106930r3 | \([1, 1, 1, -1524481, -725122961]\) | \(16232905099479601/4052240\) | \(97811222604560\) | \([2]\) | \(1327104\) | \(2.0601\) | |
| 106930.w2 | 106930r4 | \([1, 1, 1, -1518701, -730886777]\) | \(-16048965315233521/256572640900\) | \(-6193039823235972100\) | \([2]\) | \(2654208\) | \(2.4067\) | |
| 106930.w3 | 106930r1 | \([1, 1, 1, -21681, -680881]\) | \(46694890801/18944000\) | \(457262107136000\) | \([2]\) | \(442368\) | \(1.5108\) | \(\Gamma_0(N)\)-optimal |
| 106930.w4 | 106930r2 | \([1, 1, 1, 70799, -4860977]\) | \(1625964918479/1369000000\) | \(-33044331961000000\) | \([2]\) | \(884736\) | \(1.8574\) |
Rank
sage: E.rank()
The elliptic curves in class 106930.w have rank \(0\).
Complex multiplication
The elliptic curves in class 106930.w do not have complex multiplication.Modular form 106930.2.a.w
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.
