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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 6930.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6930.bb1 | 6930bd3 | \([1, -1, 1, -234392, -43615969]\) | \(1953542217204454969/170843779260\) | \(124545115080540\) | \([2]\) | \(40960\) | \(1.7459\) | |
| 6930.bb2 | 6930bd4 | \([1, -1, 1, -84992, 9070751]\) | \(93137706732176569/5369647977540\) | \(3914473375626660\) | \([2]\) | \(40960\) | \(1.7459\) | |
| 6930.bb3 | 6930bd2 | \([1, -1, 1, -15692, -575809]\) | \(586145095611769/140040608400\) | \(102089603523600\) | \([2, 2]\) | \(20480\) | \(1.3994\) | |
| 6930.bb4 | 6930bd1 | \([1, -1, 1, 2308, -57409]\) | \(1865864036231/2993760000\) | \(-2182451040000\) | \([4]\) | \(10240\) | \(1.0528\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6930.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 6930.bb do not have complex multiplication.Modular form 6930.2.a.bb
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
