Show commands:
SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 141120gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.kx2 | 141120gb1 | \([0, 0, 0, -5292, 1333584]\) | \(-108/5\) | \(-758803748290560\) | \([2]\) | \(552960\) | \(1.5353\) | \(\Gamma_0(N)\)-optimal |
| 141120.kx1 | 141120gb2 | \([0, 0, 0, -216972, 38673936]\) | \(3721734/25\) | \(7588037482905600\) | \([2]\) | \(1105920\) | \(1.8818\) |
Rank
sage: E.rank()
The elliptic curves in class 141120gb have rank \(0\).
Complex multiplication
The elliptic curves in class 141120gb do not have complex multiplication.Modular form 141120.2.a.gb
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 Cremona 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 Cremona labels.
