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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 19950.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19950.bp1 | 19950br3 | \([1, 1, 1, -453788, 117470531]\) | \(661397832743623417/443352042\) | \(6927375656250\) | \([2]\) | \(163840\) | \(1.7800\) | |
| 19950.bp2 | 19950br2 | \([1, 1, 1, -28538, 1802531]\) | \(164503536215257/4178071044\) | \(65282360062500\) | \([2, 2]\) | \(81920\) | \(1.4334\) | |
| 19950.bp3 | 19950br1 | \([1, 1, 1, -4038, -59469]\) | \(466025146777/177366672\) | \(2771354250000\) | \([2]\) | \(40960\) | \(1.0869\) | \(\Gamma_0(N)\)-optimal |
| 19950.bp4 | 19950br4 | \([1, 1, 1, 4712, 5792531]\) | \(740480746823/927484650666\) | \(-14491947666656250\) | \([2]\) | \(163840\) | \(1.7800\) |
Rank
sage: E.rank()
The elliptic curves in class 19950.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 19950.bp do not have complex multiplication.Modular form 19950.2.a.bp
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.
