Show commands:
SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 450840.cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450840.cp1 | 450840cp1 | \([0, 1, 0, -1378915, 622752410]\) | \(152818608128/7605\) | \(14429772812154960\) | \([2]\) | \(6963200\) | \(2.1719\) | \(\Gamma_0(N)\)-optimal |
450840.cp2 | 450840cp2 | \([0, 1, 0, -1305220, 692349968]\) | \(-8100185168/2142075\) | \(-65030176140111686400\) | \([2]\) | \(13926400\) | \(2.5185\) |
Rank
sage: E.rank()
The elliptic curves in class 450840.cp have rank \(0\).
Complex multiplication
The elliptic curves in class 450840.cp do not have complex multiplication.Modular form 450840.2.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.