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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 166635bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166635.bp3 | 166635bs1 | \([1, -1, 0, -385740, -81394709]\) | \(58818484369/7455105\) | \(804541237175978505\) | \([2]\) | \(2027520\) | \(2.1649\) | \(\Gamma_0(N)\)-optimal |
| 166635.bp2 | 166635bs2 | \([1, -1, 0, -1552185, 660697600]\) | \(3832302404449/472410225\) | \(50981643702681903225\) | \([2, 2]\) | \(4055040\) | \(2.5115\) | |
| 166635.bp1 | 166635bs3 | \([1, -1, 0, -24047910, 45395696335]\) | \(14251520160844849/264449745\) | \(28538930707638864345\) | \([2]\) | \(8110080\) | \(2.8581\) | |
| 166635.bp4 | 166635bs4 | \([1, -1, 0, 2280420, 3405609301]\) | \(12152722588271/53476250625\) | \(-5771058735909178175625\) | \([2]\) | \(8110080\) | \(2.8581\) |
Rank
sage: E.rank()
The elliptic curves in class 166635bs have rank \(0\).
Complex multiplication
The elliptic curves in class 166635bs do not have complex multiplication.Modular form 166635.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
