Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 28314.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28314.y1 | 28314f2 | \([1, -1, 0, -68811, 6960905]\) | \(1033364331/676\) | \(23571873370188\) | \([2]\) | \(122880\) | \(1.5056\) | |
28314.y2 | 28314f1 | \([1, -1, 0, -3471, 152477]\) | \(-132651/208\) | \(-7252884113904\) | \([2]\) | \(61440\) | \(1.1590\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28314.y have rank \(1\).
Complex multiplication
The elliptic curves in class 28314.y do not have complex multiplication.Modular form 28314.2.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.