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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 84150.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.bi1 | 84150bb4 | \([1, -1, 0, -84804192, -291661431534]\) | \(5921450764096952391481/200074809015963750\) | \(2278977121447462089843750\) | \([2]\) | \(14155776\) | \(3.4462\) | |
| 84150.bi2 | 84150bb2 | \([1, -1, 0, -13085442, 11924037216]\) | \(21754112339458491481/7199734626562500\) | \(82009477230688476562500\) | \([2, 2]\) | \(7077888\) | \(3.0996\) | |
| 84150.bi3 | 84150bb1 | \([1, -1, 0, -11784942, 15571939716]\) | \(15891267085572193561/3334993530000\) | \(37987660677656250000\) | \([2]\) | \(3538944\) | \(2.7530\) | \(\Gamma_0(N)\)-optimal |
| 84150.bi4 | 84150bb3 | \([1, -1, 0, 37825308, 82028139966]\) | \(525440531549759128199/559322204589843750\) | \(-6371029486656188964843750\) | \([2]\) | \(14155776\) | \(3.4462\) |
Rank
sage: E.rank()
The elliptic curves in class 84150.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 84150.bi do not have complex multiplication.Modular form 84150.2.a.bi
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.
