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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 28611.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28611.g1 | 28611u4 | \([1, -1, 1, -381101, -90369790]\) | \(347873904937/395307\) | \(6955935741749907\) | \([2]\) | \(245760\) | \(1.9533\) | |
| 28611.g2 | 28611u2 | \([1, -1, 1, -29966, -619684]\) | \(169112377/88209\) | \(1552150950638409\) | \([2, 2]\) | \(122880\) | \(1.6067\) | |
| 28611.g3 | 28611u1 | \([1, -1, 1, -16961, 847280]\) | \(30664297/297\) | \(5226097476897\) | \([2]\) | \(61440\) | \(1.2601\) | \(\Gamma_0(N)\)-optimal |
| 28611.g4 | 28611u3 | \([1, -1, 1, 113089, -4911334]\) | \(9090072503/5845851\) | \(-102865276637763651\) | \([2]\) | \(245760\) | \(1.9533\) |
Rank
sage: E.rank()
The elliptic curves in class 28611.g have rank \(1\).
Complex multiplication
The elliptic curves in class 28611.g do not have complex multiplication.Modular form 28611.2.a.g
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.
