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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 46800cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.k3 | 46800cc1 | \([0, 0, 0, -99675, -12245750]\) | \(-63378025803/812500\) | \(-1404000000000000\) | \([2]\) | \(331776\) | \(1.7158\) | \(\Gamma_0(N)\)-optimal |
46800.k2 | 46800cc2 | \([0, 0, 0, -1599675, -778745750]\) | \(261984288445803/42250\) | \(73008000000000\) | \([2]\) | \(663552\) | \(2.0624\) | |
46800.k4 | 46800cc3 | \([0, 0, 0, 350325, -62295750]\) | \(3774555693/3515200\) | \(-4428139622400000000\) | \([2]\) | \(995328\) | \(2.2651\) | |
46800.k1 | 46800cc4 | \([0, 0, 0, -1809675, -561255750]\) | \(520300455507/193072360\) | \(243215568760320000000\) | \([2]\) | \(1990656\) | \(2.6117\) |
Rank
sage: E.rank()
The elliptic curves in class 46800cc have rank \(0\).
Complex multiplication
The elliptic curves in class 46800cc do not have complex multiplication.Modular form 46800.2.a.cc
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 Cremona 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 Cremona labels.