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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 15730.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15730.c1 | 15730f4 | \([1, 0, 1, -2832129, 1834254002]\) | \(1418098748958579169/8307406250\) | \(14717076923656250\) | \([2]\) | \(552960\) | \(2.2920\) | |
15730.c2 | 15730f3 | \([1, 0, 1, -173759, 29752446]\) | \(-327495950129089/26547449500\) | \(-47030426183669500\) | \([2]\) | \(276480\) | \(1.9454\) | |
15730.c3 | 15730f2 | \([1, 0, 1, -50339, 88086]\) | \(7962857630209/4606058600\) | \(8159913779474600\) | \([2]\) | \(184320\) | \(1.7426\) | |
15730.c4 | 15730f1 | \([1, 0, 1, 12581, 12582]\) | \(124326214271/71980480\) | \(-127517811129280\) | \([2]\) | \(92160\) | \(1.3961\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15730.c have rank \(0\).
Complex multiplication
The elliptic curves in class 15730.c do not have complex multiplication.Modular form 15730.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.