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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 117113.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117113.c1 | 117113c4 | \([1, -1, 0, -624746, 190221759]\) | \(82483294977/17\) | \(5557986347273\) | \([2]\) | \(577280\) | \(1.8328\) | |
| 117113.c2 | 117113c2 | \([1, -1, 0, -39181, 2958072]\) | \(20346417/289\) | \(94485767903641\) | \([2, 2]\) | \(288640\) | \(1.4862\) | |
| 117113.c3 | 117113c1 | \([1, -1, 0, -4736, -52421]\) | \(35937/17\) | \(5557986347273\) | \([2]\) | \(144320\) | \(1.1396\) | \(\Gamma_0(N)\)-optimal |
| 117113.c4 | 117113c3 | \([1, -1, 0, -4736, 7952597]\) | \(-35937/83521\) | \(-27306386924152249\) | \([2]\) | \(577280\) | \(1.8328\) |
Rank
sage: E.rank()
The elliptic curves in class 117113.c have rank \(1\).
Complex multiplication
The elliptic curves in class 117113.c do not have complex multiplication.Modular form 117113.2.a.c
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.
