Show commands:
SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 19600.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19600.bo1 | 19600ch4 | \([0, -1, 0, -2460208, -1484481088]\) | \(-349938025/8\) | \(-37647680000000000\) | \([]\) | \(259200\) | \(2.2940\) | |
| 19600.bo2 | 19600ch3 | \([0, -1, 0, -10208, -4681088]\) | \(-25/2\) | \(-9411920000000000\) | \([]\) | \(86400\) | \(1.7447\) | |
| 19600.bo3 | 19600ch1 | \([0, -1, 0, -2368, 54272]\) | \(-121945/32\) | \(-385512243200\) | \([]\) | \(17280\) | \(0.94000\) | \(\Gamma_0(N)\)-optimal |
| 19600.bo4 | 19600ch2 | \([0, -1, 0, 17232, -400448]\) | \(46969655/32768\) | \(-394764537036800\) | \([]\) | \(51840\) | \(1.4893\) |
Rank
sage: E.rank()
The elliptic curves in class 19600.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 19600.bo do not have complex multiplication.Modular form 19600.2.a.bo
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
