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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 166410.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166410.bx1 | 166410bc2 | \([1, -1, 1, -5369843, 4789733527]\) | \(137627865747/36980\) | \(4601176921280409660\) | \([2]\) | \(5677056\) | \(2.5646\) | |
| 166410.bx2 | 166410bc1 | \([1, -1, 1, -377543, 55036207]\) | \(47832147/17200\) | \(2140082288967632400\) | \([2]\) | \(2838528\) | \(2.2180\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 166410.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 166410.bx do not have complex multiplication.Modular form 166410.2.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.
