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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 269790bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
269790.bs3 | 269790bs1 | \([1, 1, 1, -53440, -4174495]\) | \(114013572049/15667200\) | \(2319307880140800\) | \([2]\) | \(2365440\) | \(1.6751\) | \(\Gamma_0(N)\)-optimal |
269790.bs2 | 269790bs2 | \([1, 1, 1, -222720, 36181857]\) | \(8253429989329/936360000\) | \(138614885024040000\) | \([2, 2]\) | \(4730880\) | \(2.0217\) | |
269790.bs1 | 269790bs3 | \([1, 1, 1, -3460200, 2475946785]\) | \(30949975477232209/478125000\) | \(70779659428125000\) | \([2]\) | \(9461760\) | \(2.3683\) | |
269790.bs4 | 269790bs4 | \([1, 1, 1, 306280, 182609057]\) | \(21464092074671/109596256200\) | \(-16224179217638761800\) | \([2]\) | \(9461760\) | \(2.3683\) |
Rank
sage: E.rank()
The elliptic curves in class 269790bs have rank \(0\).
Complex multiplication
The elliptic curves in class 269790bs do not have complex multiplication.Modular form 269790.2.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 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.