Show commands:
SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 38720.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38720.bs1 | 38720f4 | \([0, 0, 0, -51788, 4536048]\) | \(132304644/5\) | \(580505108480\) | \([2]\) | \(81920\) | \(1.3433\) | |
| 38720.bs2 | 38720f2 | \([0, 0, 0, -3388, 63888]\) | \(148176/25\) | \(725631385600\) | \([2, 2]\) | \(40960\) | \(0.99673\) | |
| 38720.bs3 | 38720f1 | \([0, 0, 0, -968, -10648]\) | \(55296/5\) | \(9070392320\) | \([2]\) | \(20480\) | \(0.65016\) | \(\Gamma_0(N)\)-optimal |
| 38720.bs4 | 38720f3 | \([0, 0, 0, 6292, 362032]\) | \(237276/625\) | \(-72563138560000\) | \([2]\) | \(81920\) | \(1.3433\) |
Rank
sage: E.rank()
The elliptic curves in class 38720.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 38720.bs do not have complex multiplication.Modular form 38720.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
