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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 15210.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15210.bp1 | 15210bm3 | \([1, -1, 1, -2109152, 1179516511]\) | \(294889639316481/260\) | \(914873377860\) | \([2]\) | \(172032\) | \(2.0276\) | |
| 15210.bp2 | 15210bm2 | \([1, -1, 1, -131852, 18445951]\) | \(72043225281/67600\) | \(237867078243600\) | \([2, 2]\) | \(86016\) | \(1.6810\) | |
| 15210.bp3 | 15210bm4 | \([1, -1, 1, -101432, 27158239]\) | \(-32798729601/71402500\) | \(-251247101394802500\) | \([2]\) | \(172032\) | \(2.0276\) | |
| 15210.bp4 | 15210bm1 | \([1, -1, 1, -10172, 145279]\) | \(33076161/16640\) | \(58551896183040\) | \([2]\) | \(43008\) | \(1.3344\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15210.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 15210.bp do not have complex multiplication.Modular form 15210.2.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.
