Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 86490.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 86490.x1 | 86490bg2 | \([1, -1, 0, -5717169, -5260189167]\) | \(31942518433489/27900\) | \(18051026118227100\) | \([2]\) | \(2457600\) | \(2.4197\) | |
| 86490.x2 | 86490bg1 | \([1, -1, 0, -354789, -83347515]\) | \(-7633736209/230640\) | \(-149221815910677360\) | \([2]\) | \(1228800\) | \(2.0732\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86490.x have rank \(0\).
Complex multiplication
The elliptic curves in class 86490.x do not have complex multiplication.Modular form 86490.2.a.x
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.
