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SageMath
E = EllipticCurve("jl1")
E.isogeny_class()
Elliptic curves in class 177450.jl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177450.jl1 | 177450x6 | \([1, 0, 0, -70980088, -230178138958]\) | \(524388516989299201/3150\) | \(237569505468750\) | \([2]\) | \(14155776\) | \(2.8240\) | |
| 177450.jl2 | 177450x4 | \([1, 0, 0, -4436338, -3596670208]\) | \(128031684631201/9922500\) | \(748343942226562500\) | \([2, 2]\) | \(7077888\) | \(2.4774\) | |
| 177450.jl3 | 177450x5 | \([1, 0, 0, -4140588, -4096783458]\) | \(-104094944089921/35880468750\) | \(-2706065148229980468750\) | \([2]\) | \(14155776\) | \(2.8240\) | |
| 177450.jl4 | 177450x3 | \([1, 0, 0, -1563338, 710970792]\) | \(5602762882081/345888060\) | \(26086493765633437500\) | \([2]\) | \(7077888\) | \(2.4774\) | |
| 177450.jl5 | 177450x2 | \([1, 0, 0, -295838, -48261708]\) | \(37966934881/8643600\) | \(651890723006250000\) | \([2, 2]\) | \(3538944\) | \(2.1308\) | |
| 177450.jl6 | 177450x1 | \([1, 0, 0, 42162, -4659708]\) | \(109902239/188160\) | \(-14190818460000000\) | \([2]\) | \(1769472\) | \(1.7842\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 177450.jl have rank \(0\).
Complex multiplication
The elliptic curves in class 177450.jl do not have complex multiplication.Modular form 177450.2.a.jl
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.
