Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 116688.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116688.y1 | 116688u1 | \([0, 1, 0, -1349408, 602853876]\) | \(66342819962001390625/4812668669952\) | \(19712690872123392\) | \([2]\) | \(1419264\) | \(2.1778\) | \(\Gamma_0(N)\)-optimal |
116688.y2 | 116688u2 | \([0, 1, 0, -1262368, 684079604]\) | \(-54315282059491182625/17983956399469632\) | \(-73662285412227612672\) | \([2]\) | \(2838528\) | \(2.5244\) |
Rank
sage: E.rank()
The elliptic curves in class 116688.y have rank \(1\).
Complex multiplication
The elliptic curves in class 116688.y do not have complex multiplication.Modular form 116688.2.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.