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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 15600.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.bl1 | 15600by2 | \([0, -1, 0, -56368, -5115968]\) | \(38686490446661/141927552\) | \(72666906624000\) | \([2]\) | \(86016\) | \(1.5202\) | |
| 15600.bl2 | 15600by1 | \([0, -1, 0, -5168, 4032]\) | \(29819839301/17252352\) | \(8833204224000\) | \([2]\) | \(43008\) | \(1.1736\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15600.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 15600.bl do not have complex multiplication.Modular form 15600.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
