Show commands:
SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 27600.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27600.cp1 | 27600cu2 | \([0, 1, 0, -314408, 46891188]\) | \(53706380371489/16171875000\) | \(1035000000000000000\) | \([2]\) | \(276480\) | \(2.1620\) | |
| 27600.cp2 | 27600cu1 | \([0, 1, 0, 53592, 4939188]\) | \(265971760991/317400000\) | \(-20313600000000000\) | \([2]\) | \(138240\) | \(1.8154\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27600.cp have rank \(0\).
Complex multiplication
The elliptic curves in class 27600.cp do not have complex multiplication.Modular form 27600.2.a.cp
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.
