Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 11592.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11592.h1 | 11592e2 | \([0, 0, 0, -24051, -1358674]\) | \(1030541881826/62236321\) | \(92918329362432\) | \([2]\) | \(23040\) | \(1.4327\) | |
11592.h2 | 11592e1 | \([0, 0, 0, -23691, -1403530]\) | \(1969910093092/7889\) | \(5889106944\) | \([2]\) | \(11520\) | \(1.0861\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11592.h have rank \(1\).
Complex multiplication
The elliptic curves in class 11592.h do not have complex multiplication.Modular form 11592.2.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.