Show commands:
SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 20800.cm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20800.cm1 | 20800bi2 | \([0, 0, 0, -940, 10800]\) | \(5606442/169\) | \(2768896000\) | \([2]\) | \(10240\) | \(0.58823\) | |
| 20800.cm2 | 20800bi1 | \([0, 0, 0, -140, -400]\) | \(37044/13\) | \(106496000\) | \([2]\) | \(5120\) | \(0.24165\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20800.cm have rank \(0\).
Complex multiplication
The elliptic curves in class 20800.cm do not have complex multiplication.Modular form 20800.2.a.cm
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.
