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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 416955.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
416955.bs1 | 416955bs5 | \([1, 1, 0, -1100761207, 14056384132276]\) | \(3135316978843283198764801/571725\) | \(26897306314725\) | \([2]\) | \(53084160\) | \(3.3714\) | \(\Gamma_0(N)\)-optimal* |
416955.bs2 | 416955bs3 | \([1, 1, 0, -68797582, 219609455551]\) | \(765458482133960722801/326869475625\) | \(15377862452786150625\) | \([2, 2]\) | \(26542080\) | \(3.0248\) | \(\Gamma_0(N)\)-optimal* |
416955.bs3 | 416955bs6 | \([1, 1, 0, -68456437, 221895604654]\) | \(-754127868744065783521/15825714261328125\) | \(-744534669878445870703125\) | \([2]\) | \(53084160\) | \(3.3714\) | |
416955.bs4 | 416955bs4 | \([1, 1, 0, -9185652, -5654617371]\) | \(1821931919215868881/761147600816295\) | \(35808859451438917430895\) | \([2]\) | \(26542080\) | \(3.0248\) | |
416955.bs5 | 416955bs2 | \([1, 1, 0, -4321177, 3394279024]\) | \(189674274234120481/3859869269025\) | \(181590950306107136025\) | \([2, 2]\) | \(13271040\) | \(2.6782\) | \(\Gamma_0(N)\)-optimal* |
416955.bs6 | 416955bs1 | \([1, 1, 0, 12628, 158660211]\) | \(4733169839/231139696095\) | \(-10874170636861534695\) | \([2]\) | \(6635520\) | \(2.3316\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 416955.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 416955.bs do not have complex multiplication.Modular form 416955.2.a.bs
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.