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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 116160.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116160.bf1 | 116160m4 | \([0, -1, 0, -77601, -8294559]\) | \(890277128/15\) | \(870757662720\) | \([2]\) | \(368640\) | \(1.4213\) | |
| 116160.bf2 | 116160m3 | \([0, -1, 0, -19521, 928545]\) | \(14172488/1875\) | \(108844707840000\) | \([2]\) | \(368640\) | \(1.4213\) | |
| 116160.bf3 | 116160m2 | \([0, -1, 0, -5001, -119799]\) | \(1906624/225\) | \(1632670617600\) | \([2, 2]\) | \(184320\) | \(1.0748\) | |
| 116160.bf4 | 116160m1 | \([0, -1, 0, 444, -9810]\) | \(85184/405\) | \(-45918861120\) | \([2]\) | \(92160\) | \(0.72818\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116160.bf have rank \(2\).
Complex multiplication
The elliptic curves in class 116160.bf do not have complex multiplication.Modular form 116160.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
