Show commands for:
SageMath
sage: E = EllipticCurve("k1")
sage: E.isogeny_class()
Elliptic curves in class 35520.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 35520.k1 | 35520bq4 | [0, -1, 0, -21824321, -39235457055] | [2] | 1327104 | |
| 35520.k2 | 35520bq6 | [0, -1, 0, -19400001, 32752486881] | [2] | 2654208 | |
| 35520.k3 | 35520bq3 | [0, -1, 0, -1876801, -110522399] | [2, 2] | 1327104 | |
| 35520.k4 | 35520bq2 | [0, -1, 0, -1364801, -611975199] | [2, 2] | 663552 | |
| 35520.k5 | 35520bq1 | [0, -1, 0, -54081, -16646175] | [2] | 331776 | \(\Gamma_0(N)\)-optimal |
| 35520.k6 | 35520bq5 | [0, -1, 0, 7454399, -888744479] | [2] | 2654208 |
Rank
sage: E.rank()
The elliptic curves in class 35520.k have rank \(0\).
Complex multiplication
The elliptic curves in class 35520.k do not have complex multiplication.Modular form 35520.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
