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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 201977.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 201977.a1 | 201977a4 | \([1, -1, 0, -1077458, -430206369]\) | \(82483294977/17\) | \(28510701884297\) | \([2]\) | \(1302912\) | \(1.9690\) | |
| 201977.a2 | 201977a2 | \([1, -1, 0, -67573, -6660600]\) | \(20346417/289\) | \(484681932033049\) | \([2, 2]\) | \(651456\) | \(1.6225\) | |
| 201977.a3 | 201977a3 | \([1, -1, 0, -8168, -18006955]\) | \(-35937/83521\) | \(-140073078357551161\) | \([2]\) | \(1302912\) | \(1.9690\) | |
| 201977.a4 | 201977a1 | \([1, -1, 0, -8168, 123451]\) | \(35937/17\) | \(28510701884297\) | \([2]\) | \(325728\) | \(1.2759\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 201977.a have rank \(1\).
Complex multiplication
The elliptic curves in class 201977.a do not have complex multiplication.Modular form 201977.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
