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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 165048bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 165048.l1 | 165048bl1 | \([0, -1, 0, -1763, 13656]\) | \(256000/117\) | \(277123184208\) | \([2]\) | \(197120\) | \(0.89057\) | \(\Gamma_0(N)\)-optimal |
| 165048.l2 | 165048bl2 | \([0, -1, 0, 6172, 96180]\) | \(686000/507\) | \(-19213874105088\) | \([2]\) | \(394240\) | \(1.2371\) |
Rank
sage: E.rank()
The elliptic curves in class 165048bl have rank \(0\).
Complex multiplication
The elliptic curves in class 165048bl do not have complex multiplication.Modular form 165048.2.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 Cremona 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 Cremona labels.
