Show commands:
SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 53040.cx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53040.cx1 | 53040cq1 | \([0, 1, 0, -217920, -38781900]\) | \(279419703685750081/3666124800000\) | \(15016447180800000\) | \([2]\) | \(368640\) | \(1.9117\) | \(\Gamma_0(N)\)-optimal |
| 53040.cx2 | 53040cq2 | \([0, 1, 0, -33600, -102114252]\) | \(-1024222994222401/1098922500000000\) | \(-4501186560000000000\) | \([2]\) | \(737280\) | \(2.2583\) |
Rank
sage: E.rank()
The elliptic curves in class 53040.cx have rank \(0\).
Complex multiplication
The elliptic curves in class 53040.cx do not have complex multiplication.Modular form 53040.2.a.cx
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
