Properties

Label 46800.k
Number of curves $4$
Conductor $46800$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.k1 46800cc4 \([0, 0, 0, -1809675, -561255750]\) \(520300455507/193072360\) \(243215568760320000000\) \([2]\) \(1990656\) \(2.6117\)  
46800.k2 46800cc2 \([0, 0, 0, -1599675, -778745750]\) \(261984288445803/42250\) \(73008000000000\) \([2]\) \(663552\) \(2.0624\)  
46800.k3 46800cc1 \([0, 0, 0, -99675, -12245750]\) \(-63378025803/812500\) \(-1404000000000000\) \([2]\) \(331776\) \(1.7158\) \(\Gamma_0(N)\)-optimal
46800.k4 46800cc3 \([0, 0, 0, 350325, -62295750]\) \(3774555693/3515200\) \(-4428139622400000000\) \([2]\) \(995328\) \(2.2651\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46800.k have rank \(0\).

Complex multiplication

The elliptic curves in class 46800.k do not have complex multiplication.

Modular form 46800.2.a.k

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.