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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 8190.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8190.bw1 | 8190bu4 | \([1, -1, 1, -132017, 18495209]\) | \(349046010201856969/7245875000\) | \(5282242875000\) | \([6]\) | \(41472\) | \(1.5600\) | |
| 8190.bw2 | 8190bu3 | \([1, -1, 1, -8537, 269561]\) | \(94376601570889/12235496000\) | \(8919676584000\) | \([6]\) | \(20736\) | \(1.2135\) | |
| 8190.bw3 | 8190bu2 | \([1, -1, 1, -2732, -12319]\) | \(3092354182009/1689383150\) | \(1231560316350\) | \([2]\) | \(13824\) | \(1.0107\) | |
| 8190.bw4 | 8190bu1 | \([1, -1, 1, -2102, -36511]\) | \(1408317602329/2153060\) | \(1569580740\) | \([2]\) | \(6912\) | \(0.66414\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8190.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 8190.bw do not have complex multiplication.Modular form 8190.2.a.bw
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
