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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 11552.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality | CM discriminant |
|---|---|---|---|---|---|---|---|---|---|
| 11552.h1 | 11552h2 | \([0, 0, 0, -3971, -96026]\) | \(287496\) | \(24087491072\) | \([2]\) | \(7200\) | \(0.85483\) | \(-16\) | |
| 11552.h2 | 11552h3 | \([0, 0, 0, -3971, 96026]\) | \(287496\) | \(24087491072\) | \([2]\) | \(7200\) | \(0.85483\) | \(-16\) | |
| 11552.h3 | 11552h1 | \([0, 0, 0, -361, 0]\) | \(1728\) | \(3010936384\) | \([2, 2]\) | \(3600\) | \(0.50826\) | \(\Gamma_0(N)\)-optimal | \(-4\) |
| 11552.h4 | 11552h4 | \([0, 0, 0, 1444, 0]\) | \(1728\) | \(-192699928576\) | \([2]\) | \(7200\) | \(0.85483\) | \(-4\) |
Rank
sage: E.rank()
The elliptic curves in class 11552.h have rank \(0\).
Complex multiplication
Each elliptic curve in class 11552.h has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).Modular form 11552.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
