Show commands:
SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 193600.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193600.cj1 | 193600bl1 | \([0, -1, 0, -17137633, 27573483137]\) | \(-76711450249/851840\) | \(-6181218395095040000000\) | \([]\) | \(15482880\) | \(2.9962\) | \(\Gamma_0(N)\)-optimal |
| 193600.cj2 | 193600bl2 | \([0, -1, 0, 57398367, 142880675137]\) | \(2882081488391/2883584000\) | \(-20924190534139904000000000\) | \([]\) | \(46448640\) | \(3.5455\) |
Rank
sage: E.rank()
The elliptic curves in class 193600.cj have rank \(1\).
Complex multiplication
The elliptic curves in class 193600.cj do not have complex multiplication.Modular form 193600.2.a.cj
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
