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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 230640bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230640.bs3 | 230640bs1 | \([0, 1, 0, -3744376, 2787271124]\) | \(1597099875769/186000\) | \(676150004391936000\) | \([2]\) | \(6635520\) | \(2.4476\) | \(\Gamma_0(N)\)-optimal |
| 230640.bs2 | 230640bs2 | \([0, 1, 0, -4051896, 2302250580]\) | \(2023804595449/540562500\) | \(1965060950264064000000\) | \([2, 2]\) | \(13271040\) | \(2.7942\) | |
| 230640.bs4 | 230640bs3 | \([0, 1, 0, 10247784, 14926008084]\) | \(32740359775271/45410156250\) | \(-165075684666000000000000\) | \([2]\) | \(26542080\) | \(3.1407\) | |
| 230640.bs1 | 230640bs4 | \([0, 1, 0, -23271896, -41357901420]\) | \(383432500775449/18701300250\) | \(67983248635335558144000\) | \([2]\) | \(26542080\) | \(3.1407\) |
Rank
sage: E.rank()
The elliptic curves in class 230640bs have rank \(0\).
Complex multiplication
The elliptic curves in class 230640bs do not have complex multiplication.Modular form 230640.2.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.
