Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 336350.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
336350.y1 | 336350y2 | \([1, 0, 1, -43746, 4944798]\) | \(-417267265/235298\) | \(-5220696028298450\) | \([]\) | \(2177280\) | \(1.7191\) | |
336350.y2 | 336350y1 | \([1, 0, 1, 4304, -90842]\) | \(397535/392\) | \(-8697536073800\) | \([]\) | \(725760\) | \(1.1698\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 336350.y have rank \(0\).
Complex multiplication
The elliptic curves in class 336350.y do not have complex multiplication.Modular form 336350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.