Show commands:
SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 355488.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355488.bx1 | 355488bx2 | \([0, 1, 0, -17633, 844911]\) | \(1000000/63\) | \(38200365084672\) | \([2]\) | \(760320\) | \(1.3572\) | |
| 355488.bx2 | 355488bx1 | \([0, 1, 0, 882, 56172]\) | \(8000/147\) | \(-1392721643712\) | \([2]\) | \(380160\) | \(1.0106\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 355488.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 355488.bx do not have complex multiplication.Modular form 355488.2.a.bx
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.
