Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 190575.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.u1 | 190575br2 | \([1, -1, 1, -13955855, -14896629228]\) | \(19827475353801179/5148111413025\) | \(78050114936667882421875\) | \([2]\) | \(15482880\) | \(3.1017\) | |
| 190575.u2 | 190575br1 | \([1, -1, 1, -4934480, 4030215522]\) | \(876440017817099/44659644435\) | \(677081380244313515625\) | \([2]\) | \(7741440\) | \(2.7551\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190575.u have rank \(0\).
Complex multiplication
The elliptic curves in class 190575.u do not have complex multiplication.Modular form 190575.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
