Show commands:
SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 222768.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
222768.be1 | 222768cv2 | \([0, 0, 0, -8811, 121690]\) | \(684030715731/338005577\) | \(37380712771584\) | \([2]\) | \(491520\) | \(1.2974\) | |
222768.be2 | 222768cv1 | \([0, 0, 0, -4731, -123926]\) | \(105890949891/1288651\) | \(142514491392\) | \([2]\) | \(245760\) | \(0.95087\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 222768.be have rank \(0\).
Complex multiplication
The elliptic curves in class 222768.be do not have complex multiplication.Modular form 222768.2.a.be
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.