Show commands:
SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 290400.cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 290400.cb1 | 290400cb4 | \([0, -1, 0, -485008, -129844988]\) | \(890277128/15\) | \(212587320000000\) | \([2]\) | \(2211840\) | \(1.8795\) | |
| 290400.cb2 | 290400cb2 | \([0, -1, 0, -122008, 14447512]\) | \(14172488/1875\) | \(26573415000000000\) | \([2]\) | \(2211840\) | \(1.8795\) | |
| 290400.cb3 | 290400cb1 | \([0, -1, 0, -31258, -1887488]\) | \(1906624/225\) | \(398601225000000\) | \([2, 2]\) | \(1105920\) | \(1.5329\) | \(\Gamma_0(N)\)-optimal |
| 290400.cb4 | 290400cb3 | \([0, -1, 0, 44367, -9676863]\) | \(85184/405\) | \(-45918861120000000\) | \([2]\) | \(2211840\) | \(1.8795\) |
Rank
sage: E.rank()
The elliptic curves in class 290400.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 290400.cb do not have complex multiplication.Modular form 290400.2.a.cb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
