Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2100.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2100.h1 | 2100e1 | \([0, -1, 0, -133, 262]\) | \(1048576/525\) | \(131250000\) | \([2]\) | \(576\) | \(0.25051\) | \(\Gamma_0(N)\)-optimal |
2100.h2 | 2100e2 | \([0, -1, 0, 492, 1512]\) | \(3286064/2205\) | \(-8820000000\) | \([2]\) | \(1152\) | \(0.59708\) |
Rank
sage: E.rank()
The elliptic curves in class 2100.h have rank \(1\).
Complex multiplication
The elliptic curves in class 2100.h do not have complex multiplication.Modular form 2100.2.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.