Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 28322.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28322.j1 | 28322b1 | \([1, 1, 0, -64019, 7031879]\) | \(-208537/34\) | \(-4731041584898146\) | \([]\) | \(241920\) | \(1.7353\) | \(\Gamma_0(N)\)-optimal |
28322.j2 | 28322b2 | \([1, 1, 0, 431616, -27166936]\) | \(63905303/39304\) | \(-5469084072142256776\) | \([]\) | \(725760\) | \(2.2846\) |
Rank
sage: E.rank()
The elliptic curves in class 28322.j have rank \(1\).
Complex multiplication
The elliptic curves in class 28322.j do not have complex multiplication.Modular form 28322.2.a.j
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.