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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 11560.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11560.h1 | 11560j3 | \([0, 0, 0, -336107, -73390394]\) | \(84944038338/2088025\) | \(103218887702988800\) | \([2]\) | \(73728\) | \(2.0485\) | |
| 11560.h2 | 11560j2 | \([0, 0, 0, -47107, 2269806]\) | \(467720676/180625\) | \(4464484762240000\) | \([2, 2]\) | \(36864\) | \(1.7019\) | |
| 11560.h3 | 11560j1 | \([0, 0, 0, -41327, 3232754]\) | \(1263257424/425\) | \(2626167507200\) | \([4]\) | \(18432\) | \(1.3553\) | \(\Gamma_0(N)\)-optimal |
| 11560.h4 | 11560j4 | \([0, 0, 0, 149413, 16301334]\) | \(7462174302/6640625\) | \(-328270938400000000\) | \([2]\) | \(73728\) | \(2.0485\) |
Rank
sage: E.rank()
The elliptic curves in class 11560.h have rank \(1\).
Complex multiplication
The elliptic curves in class 11560.h do not have complex multiplication.Modular form 11560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
