Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 259182.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259182.bv1 | 259182bv1 | \([1, -1, 0, -2434482, -1464882732]\) | \(-10211146482625/27965952\) | \(-4370172878901570048\) | \([]\) | \(7299072\) | \(2.4502\) | \(\Gamma_0(N)\)-optimal |
| 259182.bv2 | 259182bv2 | \([1, -1, 0, 4752918, -7482461508]\) | \(75986355677375/198700468008\) | \(-31050450072774589525992\) | \([3]\) | \(21897216\) | \(2.9995\) |
Rank
sage: E.rank()
The elliptic curves in class 259182.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 259182.bv do not have complex multiplication.Modular form 259182.2.a.bv
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
