Properties

Label 46200cu
Number of curves $4$
Conductor $46200$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46200cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46200.cr3 46200cu1 \([0, 1, 0, -14674308, -21641270112]\) \(87364831012240243408/1760913\) \(7043652000000\) \([2]\) \(1474560\) \(2.4487\) \(\Gamma_0(N)\)-optimal
46200.cr2 46200cu2 \([0, 1, 0, -14674808, -21639722112]\) \(21843440425782779332/3100814593569\) \(49613033497104000000\) \([2, 2]\) \(2949120\) \(2.7953\)  
46200.cr4 46200cu3 \([0, 1, 0, -13351808, -25698686112]\) \(-8226100326647904626/4152140742401883\) \(-132868503756860256000000\) \([2]\) \(5898240\) \(3.1419\)  
46200.cr1 46200cu4 \([0, 1, 0, -16005808, -17481678112]\) \(14171198121996897746/4077720290568771\) \(130487049298200672000000\) \([2]\) \(5898240\) \(3.1419\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46200cu have rank \(0\).

Complex multiplication

The elliptic curves in class 46200cu do not have complex multiplication.

Modular form 46200.2.a.cu

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} + q^{11} + 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.