Show commands:
SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 7200.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7200.ca1 | 7200bz1 | \([0, 0, 0, -4845, 129800]\) | \(2156689088/81\) | \(472392000\) | \([2]\) | \(6144\) | \(0.75082\) | \(\Gamma_0(N)\)-optimal |
| 7200.ca2 | 7200bz2 | \([0, 0, 0, -4620, 142400]\) | \(-29218112/6561\) | \(-2448880128000\) | \([2]\) | \(12288\) | \(1.0974\) |
Rank
sage: E.rank()
The elliptic curves in class 7200.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 7200.ca do not have complex multiplication.Modular form 7200.2.a.ca
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.
