Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 19110.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19110.n1 | 19110o3 | \([1, 1, 0, -526187, 146352501]\) | \(136948444639063849/367281893160\) | \(43210347448380840\) | \([2]\) | \(294912\) | \(2.0663\) | |
| 19110.n2 | 19110o2 | \([1, 1, 0, -45987, 275661]\) | \(91422999252649/52587662400\) | \(6186885893697600\) | \([2, 2]\) | \(147456\) | \(1.7197\) | |
| 19110.n3 | 19110o1 | \([1, 1, 0, -30307, -2035571]\) | \(26168974809769/117411840\) | \(13813385564160\) | \([2]\) | \(73728\) | \(1.3731\) | \(\Gamma_0(N)\)-optimal |
| 19110.n4 | 19110o4 | \([1, 1, 0, 183333, 2431269]\) | \(5792335463322071/3372408585000\) | \(-396760497616665000\) | \([2]\) | \(294912\) | \(2.0663\) |
Rank
sage: E.rank()
The elliptic curves in class 19110.n have rank \(0\).
Complex multiplication
The elliptic curves in class 19110.n do not have complex multiplication.Modular form 19110.2.a.n
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.
