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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 56550.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56550.h1 | 56550d4 | \([1, 1, 0, -1618025, -792766875]\) | \(29981943972267024529/4007065140000\) | \(62610392812500000\) | \([2]\) | \(921600\) | \(2.2421\) | |
| 56550.h2 | 56550d3 | \([1, 1, 0, -650025, 193465125]\) | \(1943993954077461649/87266819409120\) | \(1363544053267500000\) | \([2]\) | \(921600\) | \(2.2421\) | |
| 56550.h3 | 56550d2 | \([1, 1, 0, -110025, -10114875]\) | \(9427227449071249/2652468249600\) | \(41444816400000000\) | \([2, 2]\) | \(460800\) | \(1.8956\) | |
| 56550.h4 | 56550d1 | \([1, 1, 0, 17975, -1026875]\) | \(41102915774831/53367275520\) | \(-833863680000000\) | \([2]\) | \(230400\) | \(1.5490\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 56550.h have rank \(0\).
Complex multiplication
The elliptic curves in class 56550.h do not have complex multiplication.Modular form 56550.2.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.
