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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 47190.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47190.bs1 | 47190bs4 | \([1, 1, 1, -43978307711, -3549834660995611]\) | \(5309860874757074224246393258249/4502770931800627200\) | \(7976933374711650923059200\) | \([2]\) | \(81100800\) | \(4.5132\) | |
| 47190.bs2 | 47190bs2 | \([1, 1, 1, -2749251711, -55441282282011]\) | \(1297212465095901089487274249/1193746061037404160000\) | \(2114793965637484751093760000\) | \([2, 2]\) | \(40550400\) | \(4.1666\) | |
| 47190.bs3 | 47190bs3 | \([1, 1, 1, -2121058431, -81449237905947]\) | \(-595697118196750093952139529/1272946549598037600000000\) | \(-2255102462352449088693600000000\) | \([2]\) | \(81100800\) | \(4.5132\) | |
| 47190.bs4 | 47190bs1 | \([1, 1, 1, -211697791, -434218447387]\) | \(592265697637387401314569/296787655248366796800\) | \(525777435319451930905804800\) | \([4]\) | \(20275200\) | \(3.8200\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47190.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 47190.bs do not have complex multiplication.Modular form 47190.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
