Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 139650.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.h1 | 139650ho2 | \([1, 1, 0, -38490, -1519650]\) | \(428831641421/181752822\) | \(2672879719434750\) | \([2]\) | \(1032192\) | \(1.6569\) | |
139650.h2 | 139650ho1 | \([1, 1, 0, 8060, -169700]\) | \(3936827539/3158028\) | \(-46442354521500\) | \([2]\) | \(516096\) | \(1.3103\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139650.h have rank \(0\).
Complex multiplication
The elliptic curves in class 139650.h do not have complex multiplication.Modular form 139650.2.a.h
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.