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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 64757.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64757.h1 | 64757e4 | \([1, -1, 0, -44872133, 115693155606]\) | \(16798320881842096017/2132227789307\) | \(1268298814764078028547\) | \([4]\) | \(4515840\) | \(3.0712\) | |
| 64757.h2 | 64757e3 | \([1, -1, 0, -17800343, -27720846980]\) | \(1048626554636928177/48569076788309\) | \(28890019553125973354189\) | \([2]\) | \(4515840\) | \(3.0712\) | |
| 64757.h3 | 64757e2 | \([1, -1, 0, -3044998, 1479980775]\) | \(5249244962308257/1448621666569\) | \(861673950581127255649\) | \([2, 2]\) | \(2257920\) | \(2.7246\) | |
| 64757.h4 | 64757e1 | \([1, -1, 0, 491407, 150999776]\) | \(22062729659823/29354283343\) | \(-17460612303658242103\) | \([2]\) | \(1128960\) | \(2.3780\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64757.h have rank \(0\).
Complex multiplication
The elliptic curves in class 64757.h do not have complex multiplication.Modular form 64757.2.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.
