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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 142912.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142912.bb1 | 142912br3 | \([0, 0, 0, -13676, 615536]\) | \(8632787556744/765919\) | \(25097633792\) | \([2]\) | \(122880\) | \(1.0360\) | |
| 142912.bb2 | 142912br2 | \([0, 0, 0, -916, 8160]\) | \(20751532992/4986289\) | \(20423839744\) | \([2, 2]\) | \(61440\) | \(0.68946\) | |
| 142912.bb3 | 142912br1 | \([0, 0, 0, -311, -2004]\) | \(51978639168/2972123\) | \(190215872\) | \([2]\) | \(30720\) | \(0.34289\) | \(\Gamma_0(N)\)-optimal |
| 142912.bb4 | 142912br4 | \([0, 0, 0, 2164, 51280]\) | \(34201530936/54460637\) | \(-1784566153216\) | \([2]\) | \(122880\) | \(1.0360\) |
Rank
sage: E.rank()
The elliptic curves in class 142912.bb have rank \(2\).
Complex multiplication
The elliptic curves in class 142912.bb do not have complex multiplication.Modular form 142912.2.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.
