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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4704.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4704.c1 | 4704v3 | \([0, -1, 0, -16529, 823425]\) | \(1036433728/63\) | \(30359089152\) | \([4]\) | \(6144\) | \(1.0719\) | |
4704.c2 | 4704v2 | \([0, -1, 0, -5504, -145452]\) | \(306182024/21609\) | \(1301645947392\) | \([2]\) | \(6144\) | \(1.0719\) | |
4704.c3 | 4704v1 | \([0, -1, 0, -1094, 11544]\) | \(19248832/3969\) | \(29884728384\) | \([2, 2]\) | \(3072\) | \(0.72533\) | \(\Gamma_0(N)\)-optimal |
4704.c4 | 4704v4 | \([0, -1, 0, 2336, 66424]\) | \(23393656/45927\) | \(-2766471998976\) | \([2]\) | \(6144\) | \(1.0719\) |
Rank
sage: E.rank()
The elliptic curves in class 4704.c have rank \(1\).
Complex multiplication
The elliptic curves in class 4704.c do not have complex multiplication.Modular form 4704.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.