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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 253575.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 253575.bn1 | 253575bn4 | \([1, -1, 1, -48840980, -130956657478]\) | \(9614816895690721/34652610405\) | \(46437812140017015703125\) | \([2]\) | \(18874368\) | \(3.2106\) | |
| 253575.bn2 | 253575bn2 | \([1, -1, 1, -4465355, 40187522]\) | \(7347774183121/4251692025\) | \(5697673947982578515625\) | \([2, 2]\) | \(9437184\) | \(2.8640\) | |
| 253575.bn3 | 253575bn1 | \([1, -1, 1, -3087230, 2082568772]\) | \(2428257525121/8150625\) | \(10922617030869140625\) | \([2]\) | \(4718592\) | \(2.5174\) | \(\Gamma_0(N)\)-optimal |
| 253575.bn4 | 253575bn3 | \([1, -1, 1, 17860270, 308095022]\) | \(470166844956479/272118787605\) | \(-364665201001620784453125\) | \([2]\) | \(18874368\) | \(3.2106\) |
Rank
sage: E.rank()
The elliptic curves in class 253575.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 253575.bn do not have complex multiplication.Modular form 253575.2.a.bn
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.
