Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 176720.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176720.u1 | 176720bn4 | \([0, 0, 0, -236363, -44228598]\) | \(132304644/5\) | \(55189582484480\) | \([2]\) | \(841984\) | \(1.7229\) | |
| 176720.u2 | 176720bn2 | \([0, 0, 0, -15463, -622938]\) | \(148176/25\) | \(68986978105600\) | \([2, 2]\) | \(420992\) | \(1.3763\) | |
| 176720.u3 | 176720bn1 | \([0, 0, 0, -4418, 103823]\) | \(55296/5\) | \(862337226320\) | \([2]\) | \(210496\) | \(1.0297\) | \(\Gamma_0(N)\)-optimal |
| 176720.u4 | 176720bn3 | \([0, 0, 0, 28717, -3529982]\) | \(237276/625\) | \(-6898697810560000\) | \([2]\) | \(841984\) | \(1.7229\) |
Rank
sage: E.rank()
The elliptic curves in class 176720.u have rank \(0\).
Complex multiplication
The elliptic curves in class 176720.u do not have complex multiplication.Modular form 176720.2.a.u
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.
