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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 63525bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63525.ce3 | 63525bs1 | \([1, 0, 1, -49133626, 132557076023]\) | \(473897054735271721/779625\) | \(21580519447265625\) | \([2]\) | \(3317760\) | \(2.8260\) | \(\Gamma_0(N)\)-optimal |
| 63525.ce2 | 63525bs2 | \([1, 0, 1, -49148751, 132471377773]\) | \(474334834335054841/607815140625\) | \(16824712474074462890625\) | \([2, 2]\) | \(6635520\) | \(3.1726\) | |
| 63525.ce4 | 63525bs3 | \([1, 0, 1, -35914376, 205419252773]\) | \(-185077034913624841/551466161890875\) | \(-15264936644149381341796875\) | \([2]\) | \(13271040\) | \(3.5191\) | |
| 63525.ce1 | 63525bs4 | \([1, 0, 1, -62625126, 54038875273]\) | \(981281029968144361/522287841796875\) | \(14457262051586151123046875\) | \([2]\) | \(13271040\) | \(3.5191\) |
Rank
sage: E.rank()
The elliptic curves in class 63525bs have rank \(0\).
Complex multiplication
The elliptic curves in class 63525bs do not have complex multiplication.Modular form 63525.2.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.
