Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 51600.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51600.bj1 | 51600bs2 | \([0, -1, 0, -534408, -150188688]\) | \(263732349218689/4160250\) | \(266256000000000\) | \([2]\) | \(331776\) | \(1.9019\) | |
| 51600.bj2 | 51600bs1 | \([0, -1, 0, -34408, -2188688]\) | \(70393838689/8062500\) | \(516000000000000\) | \([2]\) | \(165888\) | \(1.5553\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51600.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 51600.bj do not have complex multiplication.Modular form 51600.2.a.bj
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.
