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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 113256bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 113256.q3 | 113256bo1 | \([0, 0, 0, -7986, 158389]\) | \(2725888/1053\) | \(21758652341712\) | \([2]\) | \(184320\) | \(1.2582\) | \(\Gamma_0(N)\)-optimal |
| 113256.q2 | 113256bo2 | \([0, 0, 0, -56991, -5124350]\) | \(61918288/1521\) | \(502866631897344\) | \([2, 2]\) | \(368640\) | \(1.6048\) | |
| 113256.q4 | 113256bo3 | \([0, 0, 0, 8349, -16192946]\) | \(48668/85683\) | \(-113312614387534848\) | \([2]\) | \(737280\) | \(1.9514\) | |
| 113256.q1 | 113256bo4 | \([0, 0, 0, -906411, -332151050]\) | \(62275269892/39\) | \(51576064809984\) | \([2]\) | \(737280\) | \(1.9514\) |
Rank
sage: E.rank()
The elliptic curves in class 113256bo have rank \(0\).
Complex multiplication
The elliptic curves in class 113256bo do not have complex multiplication.Modular form 113256.2.a.bo
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.
