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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 141120.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.bb1 | 141120dd5 | \([0, 0, 0, -474163788, 3974117369488]\) | \(524388516989299201/3150\) | \(70821683173785600\) | \([2]\) | \(18874368\) | \(3.2987\) | |
| 141120.bb2 | 141120dd3 | \([0, 0, 0, -29635788, 62093158288]\) | \(128031684631201/9922500\) | \(223088301997424640000\) | \([2, 2]\) | \(9437184\) | \(2.9522\) | |
| 141120.bb3 | 141120dd6 | \([0, 0, 0, -27660108, 70728460432]\) | \(-104094944089921/35880468750\) | \(-806703234901401600000000\) | \([2]\) | \(18874368\) | \(3.2987\) | |
| 141120.bb4 | 141120dd4 | \([0, 0, 0, -10443468, -12277759088]\) | \(5602762882081/345888060\) | \(7776626856798521917440\) | \([2]\) | \(9437184\) | \(2.9522\) | |
| 141120.bb5 | 141120dd2 | \([0, 0, 0, -1976268, 832853392]\) | \(37966934881/8643600\) | \(194334698628867686400\) | \([2, 2]\) | \(4718592\) | \(2.6056\) | |
| 141120.bb6 | 141120dd1 | \([0, 0, 0, 281652, 80514448]\) | \(109902239/188160\) | \(-4230415208247459840\) | \([2]\) | \(2359296\) | \(2.2590\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.bb do not have complex multiplication.Modular form 141120.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
