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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 176610.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176610.bs1 | 176610by6 | \([1, 0, 1, -14128818, -20442398594]\) | \(524388516989299201/3150\) | \(1873693461150\) | \([2]\) | \(6193152\) | \(2.4204\) | |
| 176610.bs2 | 176610by4 | \([1, 0, 1, -883068, -319455194]\) | \(128031684631201/9922500\) | \(5902134402622500\) | \([2, 2]\) | \(3096576\) | \(2.0738\) | |
| 176610.bs3 | 176610by5 | \([1, 0, 1, -824198, -363866722]\) | \(-104094944089921/35880468750\) | \(-21342539580911718750\) | \([2]\) | \(6193152\) | \(2.4204\) | |
| 176610.bs4 | 176610by3 | \([1, 0, 1, -311188, 63125798]\) | \(5602762882081/345888060\) | \(205742284543447260\) | \([2]\) | \(3096576\) | \(2.0738\) | |
| 176610.bs5 | 176610by2 | \([1, 0, 1, -58888, -4288762]\) | \(37966934881/8643600\) | \(5141414857395600\) | \([2, 2]\) | \(1548288\) | \(1.7273\) | |
| 176610.bs6 | 176610by1 | \([1, 0, 1, 8392, -413434]\) | \(109902239/188160\) | \(-111921956079360\) | \([2]\) | \(774144\) | \(1.3807\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176610.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 176610.bs do not have complex multiplication.Modular form 176610.2.a.bs
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.
