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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 22050bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22050.k2 | 22050bo1 | \([1, -1, 0, 258858, -62237484]\) | \(596183/864\) | \(-2779980163033500000\) | \([]\) | \(362880\) | \(2.2246\) | \(\Gamma_0(N)\)-optimal |
| 22050.k1 | 22050bo2 | \([1, -1, 0, -7844517, -8497850859]\) | \(-16591834777/98304\) | \(-316299965216256000000\) | \([]\) | \(1088640\) | \(2.7739\) |
Rank
sage: E.rank()
The elliptic curves in class 22050bo have rank \(1\).
Complex multiplication
The elliptic curves in class 22050bo do not have complex multiplication.Modular form 22050.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
