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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 20160fh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.ei5 | 20160fh1 | \([0, 0, 0, -552, 20536]\) | \(-24918016/229635\) | \(-171421608960\) | \([2]\) | \(16384\) | \(0.83807\) | \(\Gamma_0(N)\)-optimal |
| 20160.ei4 | 20160fh2 | \([0, 0, 0, -15132, 714544]\) | \(32082281296/99225\) | \(1185137049600\) | \([2, 2]\) | \(32768\) | \(1.1846\) | |
| 20160.ei3 | 20160fh3 | \([0, 0, 0, -21612, 43216]\) | \(23366901604/13505625\) | \(645241282560000\) | \([2, 2]\) | \(65536\) | \(1.5312\) | |
| 20160.ei1 | 20160fh4 | \([0, 0, 0, -241932, 45802384]\) | \(32779037733124/315\) | \(15049359360\) | \([2]\) | \(65536\) | \(1.5312\) | |
| 20160.ei2 | 20160fh5 | \([0, 0, 0, -233292, -43224176]\) | \(14695548366242/57421875\) | \(5486745600000000\) | \([2]\) | \(131072\) | \(1.8778\) | |
| 20160.ei6 | 20160fh6 | \([0, 0, 0, 86388, 345616]\) | \(746185003198/432360075\) | \(-41312648518041600\) | \([4]\) | \(131072\) | \(1.8778\) |
Rank
sage: E.rank()
The elliptic curves in class 20160fh have rank \(1\).
Complex multiplication
The elliptic curves in class 20160fh do not have complex multiplication.Modular form 20160.2.a.fh
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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
