Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 6006.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6006.g1 | 6006d3 | \([1, 1, 0, -11104, 190258]\) | \(151433926001115913/71227975096278\) | \(71227975096278\) | \([2]\) | \(20480\) | \(1.3523\) | |
| 6006.g2 | 6006d2 | \([1, 1, 0, -5714, -166560]\) | \(20637789249996073/298712530116\) | \(298712530116\) | \([2, 2]\) | \(10240\) | \(1.0058\) | |
| 6006.g3 | 6006d1 | \([1, 1, 0, -5694, -167772]\) | \(20421858870283753/4372368\) | \(4372368\) | \([2]\) | \(5120\) | \(0.65918\) | \(\Gamma_0(N)\)-optimal |
| 6006.g4 | 6006d4 | \([1, 1, 0, -644, -445410]\) | \(-29609739866953/85584085761174\) | \(-85584085761174\) | \([2]\) | \(20480\) | \(1.3523\) |
Rank
sage: E.rank()
The elliptic curves in class 6006.g have rank \(0\).
Complex multiplication
The elliptic curves in class 6006.g do not have complex multiplication.Modular form 6006.2.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.
