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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 32490.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32490.bx1 | 32490ca4 | \([1, -1, 1, -1505037587, 14350715815299]\) | \(10993009831928446009969/3767761230468750000\) | \(129220824287598815917968750000\) | \([2]\) | \(49766400\) | \(4.2879\) | |
| 32490.bx2 | 32490ca2 | \([1, -1, 1, -1348305827, 19056290756451]\) | \(7903870428425797297009/886464000000\) | \(30402565814137536000000\) | \([2]\) | \(16588800\) | \(3.7386\) | |
| 32490.bx3 | 32490ca1 | \([1, -1, 1, -84054947, 299359000419]\) | \(-1914980734749238129/20440940544000\) | \(-701051639087241363456000\) | \([2]\) | \(8294400\) | \(3.3920\) | \(\Gamma_0(N)\)-optimal |
| 32490.bx4 | 32490ca3 | \([1, -1, 1, 277753693, 1558118706531]\) | \(69096190760262356111/70568821500000000\) | \(-2420259863998847053500000000\) | \([2]\) | \(24883200\) | \(3.9413\) |
Rank
sage: E.rank()
The elliptic curves in class 32490.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 32490.bx do not have complex multiplication.Modular form 32490.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
