Show commands:
SageMath
E = EllipticCurve("gg1")
E.isogeny_class()
Elliptic curves in class 166464.gg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166464.gg1 | 166464ge1 | \([0, 0, 0, -45084, -1493552]\) | \(35152/17\) | \(4901058848636928\) | \([2]\) | \(884736\) | \(1.7043\) | \(\Gamma_0(N)\)-optimal |
| 166464.gg2 | 166464ge2 | \([0, 0, 0, 162996, -11398160]\) | \(415292/289\) | \(-333272001707311104\) | \([2]\) | \(1769472\) | \(2.0509\) |
Rank
sage: E.rank()
The elliptic curves in class 166464.gg have rank \(0\).
Complex multiplication
The elliptic curves in class 166464.gg do not have complex multiplication.Modular form 166464.2.a.gg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
