Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 83790.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83790.y1 | 83790bf2 | \([1, -1, 0, -10286775, -12696353825]\) | \(1403607530712116449/39475350\) | \(3385647644617350\) | \([2]\) | \(3225600\) | \(2.4903\) | |
83790.y2 | 83790bf1 | \([1, -1, 0, -642105, -198790439]\) | \(-341370886042369/1817528220\) | \(-155882345237434620\) | \([2]\) | \(1612800\) | \(2.1438\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83790.y have rank \(1\).
Complex multiplication
The elliptic curves in class 83790.y do not have complex multiplication.Modular form 83790.2.a.y
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.