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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 190608.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190608.g1 | 190608bi3 | \([0, -1, 0, -846304, 299654080]\) | \(347873904937/395307\) | \(76175630665592832\) | \([2]\) | \(2764800\) | \(2.1527\) | |
| 190608.g2 | 190608bi2 | \([0, -1, 0, -66544, 2097664]\) | \(169112377/88209\) | \(16997867999760384\) | \([2, 2]\) | \(1382400\) | \(1.8062\) | |
| 190608.g3 | 190608bi1 | \([0, -1, 0, -37664, -2777280]\) | \(30664297/297\) | \(57231878787072\) | \([2]\) | \(691200\) | \(1.4596\) | \(\Gamma_0(N)\)-optimal |
| 190608.g4 | 190608bi4 | \([0, -1, 0, 251136, 16075584]\) | \(9090072503/5845851\) | \(-1126495070165938176\) | \([2]\) | \(2764800\) | \(2.1527\) |
Rank
sage: E.rank()
The elliptic curves in class 190608.g have rank \(1\).
Complex multiplication
The elliptic curves in class 190608.g do not have complex multiplication.Modular form 190608.2.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.
