Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 397800.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.z1 | 397800z2 | \([0, 0, 0, -493275, -28926250]\) | \(569001644066/313788397\) | \(7320055725216000000\) | \([2]\) | \(5898240\) | \(2.3103\) | |
| 397800.z2 | 397800z1 | \([0, 0, 0, -376275, -88713250]\) | \(505117359652/830297\) | \(9684584208000000\) | \([2]\) | \(2949120\) | \(1.9638\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 397800.z have rank \(0\).
Complex multiplication
The elliptic curves in class 397800.z do not have complex multiplication.Modular form 397800.2.a.z
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.
