Show commands:
SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 354025.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 354025.cp1 | 354025cp2 | \([1, 0, 1, -73666591451, 7695797480377423]\) | \(-162677523113838677\) | \(-271773988103064453125\) | \([]\) | \(318259200\) | \(4.4648\) | |
| 354025.cp2 | 354025cp1 | \([1, 0, 1, -2839576, -2005507577]\) | \(-9317\) | \(-271773988103064453125\) | \([]\) | \(8601600\) | \(2.6593\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 354025.cp have rank \(0\).
Complex multiplication
The elliptic curves in class 354025.cp do not have complex multiplication.Modular form 354025.2.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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
