Show commands:
SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 17600.cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17600.cd1 | 17600cd3 | \([0, 1, 0, -782033, 265925813]\) | \(-52893159101157376/11\) | \(-11000000\) | \([]\) | \(56000\) | \(1.6480\) | |
| 17600.cd2 | 17600cd2 | \([0, 1, 0, -1033, 22813]\) | \(-122023936/161051\) | \(-161051000000\) | \([]\) | \(11200\) | \(0.84328\) | |
| 17600.cd3 | 17600cd1 | \([0, 1, 0, -33, -187]\) | \(-4096/11\) | \(-11000000\) | \([]\) | \(2240\) | \(0.038564\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17600.cd have rank \(1\).
Complex multiplication
The elliptic curves in class 17600.cd do not have complex multiplication.Modular form 17600.2.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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
