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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 291525.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 291525.bu1 | 291525bu3 | \([1, 1, 0, -127314125, 552652387500]\) | \(3026030815665395929/1364501953125\) | \(102909223560333251953125\) | \([2]\) | \(55296000\) | \(3.3735\) | |
| 291525.bu2 | 291525bu4 | \([1, 1, 0, -69980875, -221440747250]\) | \(502552788401502649/10024505152875\) | \(756037057694428529296875\) | \([2]\) | \(55296000\) | \(3.3735\) | |
| 291525.bu3 | 291525bu2 | \([1, 1, 0, -9246500, 5645080875]\) | \(1159246431432649/488076890625\) | \(36810217630636962890625\) | \([2, 2]\) | \(27648000\) | \(3.0269\) | |
| 291525.bu4 | 291525bu1 | \([1, 1, 0, 1928625, 649800000]\) | \(10519294081031/8500170375\) | \(-641073419805990234375\) | \([2]\) | \(13824000\) | \(2.6803\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 291525.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 291525.bu do not have complex multiplication.Modular form 291525.2.a.bu
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.
