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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 58800.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.o1 | 58800bf4 | \([0, -1, 0, -8232408, 9094305312]\) | \(32779037733124/315\) | \(592950960000000\) | \([4]\) | \(1179648\) | \(2.4130\) | |
58800.o2 | 58800bf6 | \([0, -1, 0, -7938408, -8577152688]\) | \(14695548366242/57421875\) | \(216180037500000000000\) | \([2]\) | \(2359296\) | \(2.7596\) | |
58800.o3 | 58800bf3 | \([0, -1, 0, -735408, 8823312]\) | \(23366901604/13505625\) | \(25422772410000000000\) | \([2, 2]\) | \(1179648\) | \(2.4130\) | |
58800.o4 | 58800bf2 | \([0, -1, 0, -514908, 142005312]\) | \(32082281296/99225\) | \(46694888100000000\) | \([2, 2]\) | \(589824\) | \(2.0664\) | |
58800.o5 | 58800bf1 | \([0, -1, 0, -18783, 4082562]\) | \(-24918016/229635\) | \(-6754082028750000\) | \([2]\) | \(294912\) | \(1.7199\) | \(\Gamma_0(N)\)-optimal |
58800.o6 | 58800bf5 | \([0, -1, 0, 2939592, 67623312]\) | \(746185003198/432360075\) | \(-1627735374837600000000\) | \([2]\) | \(2359296\) | \(2.7596\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.o have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.o do not have complex multiplication.Modular form 58800.2.a.o
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.