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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 5808.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5808.b1 | 5808v3 | \([0, -1, 0, -19485880, -33101139344]\) | \(112763292123580561/1932612\) | \(14023639233871872\) | \([2]\) | \(288000\) | \(2.6399\) | |
| 5808.b2 | 5808v4 | \([0, -1, 0, -19466520, -33170215824]\) | \(-112427521449300721/466873642818\) | \(-3387781683381448286208\) | \([2]\) | \(576000\) | \(2.9865\) | |
| 5808.b3 | 5808v1 | \([0, -1, 0, -87160, 7248496]\) | \(10091699281/2737152\) | \(19861633983578112\) | \([2]\) | \(57600\) | \(1.8352\) | \(\Gamma_0(N)\)-optimal |
| 5808.b4 | 5808v2 | \([0, -1, 0, 222600, 46897776]\) | \(168105213359/228637728\) | \(-1659067113690759168\) | \([2]\) | \(115200\) | \(2.1818\) |
Rank
sage: E.rank()
The elliptic curves in class 5808.b have rank \(1\).
Complex multiplication
The elliptic curves in class 5808.b do not have complex multiplication.Modular form 5808.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
