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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 379050.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 379050.bf1 | 379050bf4 | \([1, 1, 0, -3371025, -2383673625]\) | \(5763259856089/5670\) | \(4167971019843750\) | \([2]\) | \(11059200\) | \(2.2905\) | |
| 379050.bf2 | 379050bf2 | \([1, 1, 0, -212275, -36722375]\) | \(1439069689/44100\) | \(32417552376562500\) | \([2, 2]\) | \(5529600\) | \(1.9439\) | |
| 379050.bf3 | 379050bf1 | \([1, 1, 0, -31775, 1363125]\) | \(4826809/1680\) | \(1234954376250000\) | \([2]\) | \(2764800\) | \(1.5974\) | \(\Gamma_0(N)\)-optimal |
| 379050.bf4 | 379050bf3 | \([1, 1, 0, 58475, -123633125]\) | \(30080231/9003750\) | \(-6618583610214843750\) | \([2]\) | \(11059200\) | \(2.2905\) |
Rank
sage: E.rank()
The elliptic curves in class 379050.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 379050.bf do not have complex multiplication.Modular form 379050.2.a.bf
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
