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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 140790bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 140790.be6 | 140790bx1 | \([1, 0, 1, 5407, -60844]\) | \(371694959/249600\) | \(-11742651897600\) | \([2]\) | \(442368\) | \(1.1966\) | \(\Gamma_0(N)\)-optimal |
| 140790.be5 | 140790bx2 | \([1, 0, 1, -23473, -511372]\) | \(30400540561/15210000\) | \(715567850010000\) | \([2, 2]\) | \(884736\) | \(1.5431\) | |
| 140790.be3 | 140790bx3 | \([1, 0, 1, -203973, 35083228]\) | \(19948814692561/231344100\) | \(10883786998652100\) | \([2, 2]\) | \(1769472\) | \(1.8897\) | |
| 140790.be2 | 140790bx4 | \([1, 0, 1, -305053, -64824244]\) | \(66730743078481/60937500\) | \(2866858373437500\) | \([2]\) | \(1769472\) | \(1.8897\) | |
| 140790.be1 | 140790bx5 | \([1, 0, 1, -3254423, 2259471368]\) | \(81025909800741361/11088090\) | \(521648962657290\) | \([2]\) | \(3538944\) | \(2.2363\) | |
| 140790.be4 | 140790bx6 | \([1, 0, 1, -41523, 89471488]\) | \(-168288035761/73415764890\) | \(-3453909338538918090\) | \([2]\) | \(3538944\) | \(2.2363\) |
Rank
sage: E.rank()
The elliptic curves in class 140790bx have rank \(0\).
Complex multiplication
The elliptic curves in class 140790bx do not have complex multiplication.Modular form 140790.2.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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
