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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 28314.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28314.h1 | 28314ba4 | \([1, -1, 0, -5439033, -4881005915]\) | \(13778603383488553/13703976\) | \(17698246051944744\) | \([2]\) | \(737280\) | \(2.4104\) | |
| 28314.h2 | 28314ba3 | \([1, -1, 0, -821673, 181554709]\) | \(47504791830313/16490207448\) | \(21296574721257233112\) | \([2]\) | \(737280\) | \(2.4104\) | |
| 28314.h3 | 28314ba2 | \([1, -1, 0, -342513, -74987555]\) | \(3440899317673/106007616\) | \(136905440534051904\) | \([2, 2]\) | \(368640\) | \(2.0638\) | |
| 28314.h4 | 28314ba1 | \([1, -1, 0, 5967, -3967331]\) | \(18191447/5271552\) | \(-6808040554917888\) | \([2]\) | \(184320\) | \(1.7172\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28314.h have rank \(2\).
Complex multiplication
The elliptic curves in class 28314.h do not have complex multiplication.Modular form 28314.2.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.
