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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 69678bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69678.bs3 | 69678bs1 | \([1, -1, 1, -20516, 1136139]\) | \(11134383337/316\) | \(27102094236\) | \([]\) | \(151200\) | \(1.1035\) | \(\Gamma_0(N)\)-optimal |
| 69678.bs2 | 69678bs2 | \([1, -1, 1, -35951, -777801]\) | \(59914169497/31554496\) | \(2706306722030016\) | \([]\) | \(453600\) | \(1.6528\) | |
| 69678.bs1 | 69678bs3 | \([1, -1, 1, -2300486, -1342427691]\) | \(15698803397448457/20709376\) | \(1776162847850496\) | \([]\) | \(1360800\) | \(2.2021\) |
Rank
sage: E.rank()
The elliptic curves in class 69678bs have rank \(1\).
Complex multiplication
The elliptic curves in class 69678bs do not have complex multiplication.Modular form 69678.2.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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
