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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 328560.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
328560.bx1 | 328560bx4 | \([0, 1, 0, -7469373976, -248472751706476]\) | \(4385367890843575421521/24975000000\) | \(262467653897318400000000\) | \([2]\) | \(226934784\) | \(4.1054\) | |
328560.bx2 | 328560bx5 | \([0, 1, 0, -6639650456, 207333307020180]\) | \(3080272010107543650001/15465841417699560\) | \(162533858356419629546209443840\) | \([2]\) | \(453869568\) | \(4.4520\) | |
328560.bx3 | 328560bx3 | \([0, 1, 0, -642335256, -703961563500]\) | \(2788936974993502801/1593609593601600\) | \(16747586436871710902904422400\) | \([2, 2]\) | \(226934784\) | \(4.1054\) | |
328560.bx4 | 328560bx2 | \([0, 1, 0, -467103256, -3877833640300]\) | \(1072487167529950801/2554882560000\) | \(26849811071326318755840000\) | \([2, 2]\) | \(113467392\) | \(3.7589\) | |
328560.bx5 | 328560bx1 | \([0, 1, 0, -18509336, -105517648236]\) | \(-66730743078481/419010969600\) | \(-4403476522448552617574400\) | \([2]\) | \(56733696\) | \(3.4123\) | \(\Gamma_0(N)\)-optimal |
328560.bx6 | 328560bx6 | \([0, 1, 0, 2551267944, -5610613519980]\) | \(174751791402194852399/102423900876336360\) | \(-1076394833474414354509542359040\) | \([2]\) | \(453869568\) | \(4.4520\) |
Rank
sage: E.rank()
The elliptic curves in class 328560.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 328560.bx do not have complex multiplication.Modular form 328560.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.