Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 114920.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 114920.h1 | 114920f4 | \([0, 0, 0, -196547, -32818786]\) | \(84944038338/2088025\) | \(20640763621836800\) | \([2]\) | \(589824\) | \(1.9143\) | |
| 114920.h2 | 114920f2 | \([0, 0, 0, -27547, 1015014]\) | \(467720676/180625\) | \(892766592640000\) | \([2, 2]\) | \(294912\) | \(1.5678\) | |
| 114920.h3 | 114920f1 | \([0, 0, 0, -24167, 1445626]\) | \(1263257424/425\) | \(525156819200\) | \([2]\) | \(147456\) | \(1.2212\) | \(\Gamma_0(N)\)-optimal |
| 114920.h4 | 114920f3 | \([0, 0, 0, 87373, 7289646]\) | \(7462174302/6640625\) | \(-65644602400000000\) | \([2]\) | \(589824\) | \(1.9143\) |
Rank
sage: E.rank()
The elliptic curves in class 114920.h have rank \(1\).
Complex multiplication
The elliptic curves in class 114920.h do not have complex multiplication.Modular form 114920.2.a.h
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.
