Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 271950.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271950.bg1 | 271950bg2 | \([1, 1, 0, -84200, 5975250]\) | \(98547108659/33734898\) | \(22599746121093750\) | \([2]\) | \(2211840\) | \(1.8400\) | |
271950.bg2 | 271950bg1 | \([1, 1, 0, -75450, 7944000]\) | \(70906537619/16428\) | \(11005476562500\) | \([2]\) | \(1105920\) | \(1.4935\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 271950.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 271950.bg do not have complex multiplication.Modular form 271950.2.a.bg
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.