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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 132600.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
132600.bb1 | 132600y4 | \([0, -1, 0, -2256008, -971537988]\) | \(79364416584061444/20404090514925\) | \(326465448238800000000\) | \([2]\) | \(4718592\) | \(2.6456\) | |
132600.bb2 | 132600y2 | \([0, -1, 0, -793508, 259887012]\) | \(13813960087661776/714574355625\) | \(2858297422500000000\) | \([2, 2]\) | \(2359296\) | \(2.2990\) | |
132600.bb3 | 132600y1 | \([0, -1, 0, -783383, 267136512]\) | \(212670222886967296/616241925\) | \(154060481250000\) | \([2]\) | \(1179648\) | \(1.9524\) | \(\Gamma_0(N)\)-optimal |
132600.bb4 | 132600y3 | \([0, -1, 0, 506992, 1027182012]\) | \(900753985478876/29018422265625\) | \(-464294756250000000000\) | \([2]\) | \(4718592\) | \(2.6456\) |
Rank
sage: E.rank()
The elliptic curves in class 132600.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 132600.bb do not have complex multiplication.Modular form 132600.2.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.