Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 16562.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16562.y1 | 16562r2 | \([1, -1, 0, -1761265, 987547679]\) | \(-1064019559329/125497034\) | \(-71265906830943946394\) | \([]\) | \(889056\) | \(2.5452\) | |
16562.y2 | 16562r1 | \([1, -1, 0, -22255, -1949011]\) | \(-2146689/1664\) | \(-944934435396224\) | \([]\) | \(127008\) | \(1.5723\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16562.y have rank \(0\).
Complex multiplication
The elliptic curves in class 16562.y do not have complex multiplication.Modular form 16562.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.