Show commands:
SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 6336.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6336.cj1 | 6336ci3 | \([0, 0, 0, -202764, -35142640]\) | \(4824238966273/66\) | \(12612796416\) | \([2]\) | \(24576\) | \(1.4941\) | |
| 6336.cj2 | 6336ci2 | \([0, 0, 0, -12684, -548080]\) | \(1180932193/4356\) | \(832444563456\) | \([2, 2]\) | \(12288\) | \(1.1475\) | |
| 6336.cj3 | 6336ci4 | \([0, 0, 0, -6924, -1048048]\) | \(-192100033/2371842\) | \(-453266064801792\) | \([2]\) | \(24576\) | \(1.4941\) | |
| 6336.cj4 | 6336ci1 | \([0, 0, 0, -1164, 272]\) | \(912673/528\) | \(100902371328\) | \([2]\) | \(6144\) | \(0.80093\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6336.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 6336.cj do not have complex multiplication.Modular form 6336.2.a.cj
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.
