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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2541.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2541.h1 | 2541b5 | \([1, 1, 0, -546801, 155401866]\) | \(10206027697760497/5557167\) | \(9844860327687\) | \([2]\) | \(19200\) | \(1.8217\) | |
| 2541.h2 | 2541b3 | \([1, 1, 0, -34366, 2388775]\) | \(2533811507137/58110129\) | \(102945638241369\) | \([2, 2]\) | \(9600\) | \(1.4752\) | |
| 2541.h3 | 2541b2 | \([1, 1, 0, -4721, -71760]\) | \(6570725617/2614689\) | \(4632081059529\) | \([2, 2]\) | \(4800\) | \(1.1286\) | |
| 2541.h4 | 2541b1 | \([1, 1, 0, -4116, -103341]\) | \(4354703137/1617\) | \(2864614137\) | \([2]\) | \(2400\) | \(0.78202\) | \(\Gamma_0(N)\)-optimal |
| 2541.h5 | 2541b6 | \([1, 1, 0, 3749, 7442824]\) | \(3288008303/13504609503\) | \(-23924239515744183\) | \([2]\) | \(19200\) | \(1.8217\) | |
| 2541.h6 | 2541b4 | \([1, 1, 0, 15244, -499011]\) | \(221115865823/190238433\) | \(-337018988603913\) | \([2]\) | \(9600\) | \(1.4752\) |
Rank
sage: E.rank()
The elliptic curves in class 2541.h have rank \(0\).
Complex multiplication
The elliptic curves in class 2541.h do not have complex multiplication.Modular form 2541.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
