Show commands:
SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 11550.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11550.cr1 | 11550cm3 | \([1, 0, 0, -74768463, 247934103417]\) | \(2958414657792917260183849/12401051653985258880\) | \(193766432093519670000000\) | \([2]\) | \(2408448\) | \(3.3231\) | |
| 11550.cr2 | 11550cm2 | \([1, 0, 0, -7008463, -406296583]\) | \(2436531580079063806249/1405478914998681600\) | \(21960608046854400000000\) | \([2, 2]\) | \(1204224\) | \(2.9765\) | |
| 11550.cr3 | 11550cm1 | \([1, 0, 0, -4960463, -4242200583]\) | \(863913648706111516969/2486234429521920\) | \(38847412961280000000\) | \([2]\) | \(602112\) | \(2.6299\) | \(\Gamma_0(N)\)-optimal |
| 11550.cr4 | 11550cm4 | \([1, 0, 0, 27983537, -3240648583]\) | \(155099895405729262880471/90047655797243760000\) | \(-1406994621831933750000000\) | \([2]\) | \(2408448\) | \(3.3231\) |
Rank
sage: E.rank()
The elliptic curves in class 11550.cr have rank \(1\).
Complex multiplication
The elliptic curves in class 11550.cr do not have complex multiplication.Modular form 11550.2.a.cr
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
