Show commands:
SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 24255.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24255.bq1 | 24255bs6 | \([1, -1, 0, -1344697209, -18979168274060]\) | \(3135316978843283198764801/571725\) | \(49034635528725\) | \([2]\) | \(2949120\) | \(3.4214\) | |
| 24255.bq2 | 24255bs4 | \([1, -1, 0, -84043584, -296533682285]\) | \(765458482133960722801/326869475625\) | \(28034326997660300625\) | \([2, 2]\) | \(1474560\) | \(3.0748\) | |
| 24255.bq3 | 24255bs5 | \([1, -1, 0, -83626839, -299620345802]\) | \(-754127868744065783521/15825714261328125\) | \(-1357310124248493589453125\) | \([4]\) | \(2949120\) | \(3.4214\) | |
| 24255.bq4 | 24255bs3 | \([1, -1, 0, -11221254, 7632484033]\) | \(1821931919215868881/761147600816295\) | \(65280677230470055741695\) | \([2]\) | \(1474560\) | \(3.0748\) | |
| 24255.bq5 | 24255bs2 | \([1, -1, 0, -5278779, -4584056072]\) | \(189674274234120481/3859869269025\) | \(331046014771379702025\) | \([2, 2]\) | \(737280\) | \(2.7283\) | |
| 24255.bq6 | 24255bs1 | \([1, -1, 0, 15426, -214219265]\) | \(4733169839/231139696095\) | \(-19823955143186997495\) | \([2]\) | \(368640\) | \(2.3817\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24255.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 24255.bq do not have complex multiplication.Modular form 24255.2.a.bq
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
