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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 63525.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63525.bs1 | 63525f4 | \([1, 1, 0, -6211900, 5956568875]\) | \(957681397954009/31185\) | \(863220777890625\) | \([2]\) | \(1105920\) | \(2.3673\) | |
| 63525.bs2 | 63525f3 | \([1, 1, 0, -615650, -28242375]\) | \(932288503609/527295615\) | \(14595880421953359375\) | \([2]\) | \(1105920\) | \(2.3673\) | |
| 63525.bs3 | 63525f2 | \([1, 1, 0, -388775, 92682000]\) | \(234770924809/1334025\) | \(36926666609765625\) | \([2, 2]\) | \(552960\) | \(2.0207\) | |
| 63525.bs4 | 63525f1 | \([1, 1, 0, -10650, 3066375]\) | \(-4826809/144375\) | \(-3996392490234375\) | \([2]\) | \(276480\) | \(1.6741\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63525.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 63525.bs 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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
