Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 225264.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 225264.bj1 | 225264cu1 | \([0, -1, 0, -235131, 41307318]\) | \(1909913257984/129730653\) | \(97652685809444688\) | \([2]\) | \(2903040\) | \(2.0086\) | \(\Gamma_0(N)\)-optimal |
| 225264.bj2 | 225264cu2 | \([0, -1, 0, 203484, 177277968]\) | \(77366117936/1172914587\) | \(-14126284821290533632\) | \([2]\) | \(5806080\) | \(2.3552\) |
Rank
sage: E.rank()
The elliptic curves in class 225264.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 225264.bj do not have complex multiplication.Modular form 225264.2.a.bj
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.
