Show commands:
SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 25410bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25410.bo3 | 25410bx1 | \([1, 1, 1, -24008641, 45156546623]\) | \(863913648706111516969/2486234429521920\) | \(4404515952198282117120\) | \([2]\) | \(3010560\) | \(3.0242\) | \(\Gamma_0(N)\)-optimal |
| 25410.bo2 | 25410bx2 | \([1, 1, 1, -33920961, 4305893439]\) | \(2436531580079063806249/1405478914998681600\) | \(2489891632133979373977600\) | \([2, 2]\) | \(6021120\) | \(3.3707\) | |
| 25410.bo4 | 25410bx3 | \([1, 1, 1, 135440319, 34587690303]\) | \(155099895405729262880471/90047655797243760000\) | \(-159524915151820952709360000\) | \([2]\) | \(12042240\) | \(3.7173\) | |
| 25410.bo1 | 25410bx4 | \([1, 1, 1, -361879361, -2640219460801]\) | \(2958414657792917260183849/12401051653985258880\) | \(21969219469185779206711680\) | \([2]\) | \(12042240\) | \(3.7173\) |
Rank
sage: E.rank()
The elliptic curves in class 25410bx have rank \(0\).
Complex multiplication
The elliptic curves in class 25410bx do not have complex multiplication.Modular form 25410.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
