Show commands:
SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 81600.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81600.cu1 | 81600ff4 | \([0, -1, 0, -297633, 62467137]\) | \(711882749089/1721250\) | \(7050240000000000\) | \([2]\) | \(589824\) | \(1.9198\) | |
| 81600.cu2 | 81600ff3 | \([0, -1, 0, -265633, -52380863]\) | \(506071034209/2505630\) | \(10263060480000000\) | \([2]\) | \(589824\) | \(1.9198\) | |
| 81600.cu3 | 81600ff2 | \([0, -1, 0, -25633, 179137]\) | \(454756609/260100\) | \(1065369600000000\) | \([2, 2]\) | \(294912\) | \(1.5732\) | |
| 81600.cu4 | 81600ff1 | \([0, -1, 0, 6367, 19137]\) | \(6967871/4080\) | \(-16711680000000\) | \([2]\) | \(147456\) | \(1.2267\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 81600.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 81600.cu do not have complex multiplication.Modular form 81600.2.a.cu
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
