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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 115600.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115600.dc1 | 115600bz4 | \([0, -1, 0, -13065208, 12565212912]\) | \(159661140625/48275138\) | \(74575646365409408000000\) | \([2]\) | \(11943936\) | \(3.0940\) | |
| 115600.dc2 | 115600bz3 | \([0, -1, 0, -11909208, 15820508912]\) | \(120920208625/19652\) | \(30358496383232000000\) | \([2]\) | \(5971968\) | \(2.7474\) | |
| 115600.dc3 | 115600bz2 | \([0, -1, 0, -4973208, -4266147088]\) | \(8805624625/2312\) | \(3571587809792000000\) | \([2]\) | \(3981312\) | \(2.5447\) | |
| 115600.dc4 | 115600bz1 | \([0, -1, 0, -349208, -49059088]\) | \(3048625/1088\) | \(1680747204608000000\) | \([2]\) | \(1990656\) | \(2.1981\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115600.dc have rank \(0\).
Complex multiplication
The elliptic curves in class 115600.dc do not have complex multiplication.Modular form 115600.2.a.dc
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.
