Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 39600.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.k1 | 39600ee4 | \([0, 0, 0, -5769075, 5333395250]\) | \(455129268177961/4392300\) | \(204927148800000000\) | \([2]\) | \(1179648\) | \(2.4832\) | |
| 39600.k2 | 39600ee2 | \([0, 0, 0, -369075, 79195250]\) | \(119168121961/10890000\) | \(508083840000000000\) | \([2, 2]\) | \(589824\) | \(2.1366\) | |
| 39600.k3 | 39600ee1 | \([0, 0, 0, -81075, -7492750]\) | \(1263214441/211200\) | \(9853747200000000\) | \([2]\) | \(294912\) | \(1.7900\) | \(\Gamma_0(N)\)-optimal |
| 39600.k4 | 39600ee3 | \([0, 0, 0, 422925, 373027250]\) | \(179310732119/1392187500\) | \(-64953900000000000000\) | \([2]\) | \(1179648\) | \(2.4832\) |
Rank
sage: E.rank()
The elliptic curves in class 39600.k have rank \(0\).
Complex multiplication
The elliptic curves in class 39600.k do not have complex multiplication.Modular form 39600.2.a.k
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.
