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SageMath
E = EllipticCurve("fi1")
E.isogeny_class()
Elliptic curves in class 106470.fi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106470.fi1 | 106470fh6 | \([1, -1, 1, -25552832, 49723588581]\) | \(524388516989299201/3150\) | \(11084042847150\) | \([2]\) | \(4718592\) | \(2.5685\) | |
106470.fi2 | 106470fh4 | \([1, -1, 1, -1597082, 777200181]\) | \(128031684631201/9922500\) | \(34914734968522500\) | \([2, 2]\) | \(2359296\) | \(2.2220\) | |
106470.fi3 | 106470fh5 | \([1, -1, 1, -1490612, 885203349]\) | \(-104094944089921/35880468750\) | \(-126254175555817968750\) | \([2]\) | \(4718592\) | \(2.5685\) | |
106470.fi4 | 106470fh3 | \([1, -1, 1, -562802, -153457131]\) | \(5602762882081/345888060\) | \(1217091453129393660\) | \([2]\) | \(2359296\) | \(2.2220\) | |
106470.fi5 | 106470fh2 | \([1, -1, 1, -106502, 10445829]\) | \(37966934881/8643600\) | \(30414613572579600\) | \([2, 2]\) | \(1179648\) | \(1.8754\) | |
106470.fi6 | 106470fh1 | \([1, -1, 1, 15178, 1003461]\) | \(109902239/188160\) | \(-662086826069760\) | \([2]\) | \(589824\) | \(1.5288\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106470.fi have rank \(0\).
Complex multiplication
The elliptic curves in class 106470.fi do not have complex multiplication.Modular form 106470.2.a.fi
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.