Show commands:
SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 48400cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48400.ba2 | 48400cd1 | \([0, -1, 0, 482992, -521703488]\) | \(109902239/1100000\) | \(-124717894400000000000\) | \([]\) | \(1382400\) | \(2.5372\) | \(\Gamma_0(N)\)-optimal |
48400.ba1 | 48400cd2 | \([0, -1, 0, -287497008, -1876186263488]\) | \(-23178622194826561/1610510\) | \(-182599469191040000000\) | \([]\) | \(6912000\) | \(3.3419\) |
Rank
sage: E.rank()
The elliptic curves in class 48400cd have rank \(1\).
Complex multiplication
The elliptic curves in class 48400cd do not have complex multiplication.Modular form 48400.2.a.cd
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.