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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 134064.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134064.bb1 | 134064k4 | \([0, 0, 0, -128077131, -557898569606]\) | \(661397832743623417/443352042\) | \(155748699667534159872\) | \([2]\) | \(11796480\) | \(3.1907\) | |
| 134064.bb2 | 134064k2 | \([0, 0, 0, -8054571, -8603321510]\) | \(164503536215257/4178071044\) | \(1467748133709006127104\) | \([2, 2]\) | \(5898240\) | \(2.8441\) | |
| 134064.bb3 | 134064k1 | \([0, 0, 0, -1139691, 274001434]\) | \(466025146777/177366672\) | \(62308562747880701952\) | \([2]\) | \(2949120\) | \(2.4976\) | \(\Gamma_0(N)\)-optimal |
| 134064.bb4 | 134064k3 | \([0, 0, 0, 1329909, -27456741830]\) | \(740480746823/927484650666\) | \(-325823532133019183456256\) | \([2]\) | \(11796480\) | \(3.1907\) |
Rank
sage: E.rank()
The elliptic curves in class 134064.bb have rank \(2\).
Complex multiplication
The elliptic curves in class 134064.bb do not have complex multiplication.Modular form 134064.2.a.bb
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.
