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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 40560.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.bx1 | 40560bz6 | \([0, 1, 0, -24376616, 46316102964]\) | \(81025909800741361/11088090\) | \(219218299309301760\) | \([2]\) | \(2064384\) | \(2.7397\) | |
| 40560.bx2 | 40560bz4 | \([0, 1, 0, -2284936, -1329123340]\) | \(66730743078481/60937500\) | \(1204771526400000000\) | \([2]\) | \(1032192\) | \(2.3931\) | |
| 40560.bx3 | 40560bz3 | \([0, 1, 0, -1527816, 719037684]\) | \(19948814692561/231344100\) | \(4573813899169382400\) | \([2, 2]\) | \(1032192\) | \(2.3931\) | |
| 40560.bx4 | 40560bz5 | \([0, 1, 0, -311016, 1834113204]\) | \(-168288035761/73415764890\) | \(-1451474430824185896960\) | \([2]\) | \(2064384\) | \(2.7397\) | |
| 40560.bx5 | 40560bz2 | \([0, 1, 0, -175816, -10501516]\) | \(30400540561/15210000\) | \(300710972989440000\) | \([2, 2]\) | \(516096\) | \(2.0465\) | |
| 40560.bx6 | 40560bz1 | \([0, 1, 0, 40504, -1243020]\) | \(371694959/249600\) | \(-4934744172134400\) | \([2]\) | \(258048\) | \(1.7000\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40560.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 40560.bx do not have complex multiplication.Modular form 40560.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
