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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 28749.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28749.h1 | 28749e6 | \([1, 0, 1, -1073325, -428090351]\) | \(53297461115137/147\) | \(377161782123\) | \([2]\) | \(202752\) | \(1.8797\) | |
| 28749.h2 | 28749e4 | \([1, 0, 1, -67110, -6687509]\) | \(13027640977/21609\) | \(55442781972081\) | \([2, 2]\) | \(101376\) | \(1.5331\) | |
| 28749.h3 | 28749e3 | \([1, 0, 1, -53420, 4718999]\) | \(6570725617/45927\) | \(117836116786143\) | \([2]\) | \(101376\) | \(1.5331\) | |
| 28749.h4 | 28749e5 | \([1, 0, 1, -46575, -10852007]\) | \(-4354703137/17294403\) | \(-44372706504988827\) | \([2]\) | \(202752\) | \(1.8797\) | |
| 28749.h5 | 28749e2 | \([1, 0, 1, -5505, -34169]\) | \(7189057/3969\) | \(10183368117321\) | \([2, 2]\) | \(50688\) | \(1.1865\) | |
| 28749.h6 | 28749e1 | \([1, 0, 1, 1340, -4051]\) | \(103823/63\) | \(-161640763767\) | \([2]\) | \(25344\) | \(0.83994\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28749.h have rank \(0\).
Complex multiplication
The elliptic curves in class 28749.h do not have complex multiplication.Modular form 28749.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
