Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.fm4 46800x1 \([0, 0, 0, -4575, 422750]\) \(-3631696/24375\) \(-71077500000000\) \([2]\) \(147456\) \(1.3413\) \(\Gamma_0(N)\)-optimal
46800.fm3 46800x2 \([0, 0, 0, -117075, 15385250]\) \(15214885924/38025\) \(443523600000000\) \([2, 2]\) \(294912\) \(1.6878\)  
46800.fm2 46800x3 \([0, 0, 0, -162075, 2470250]\) \(20183398562/11567205\) \(269839758240000000\) \([2]\) \(589824\) \(2.0344\)  
46800.fm1 46800x4 \([0, 0, 0, -1872075, 985900250]\) \(31103978031362/195\) \(4548960000000\) \([2]\) \(589824\) \(2.0344\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 46800.2.a.x

sage: E.q_eigenform(10)
 
\(q + 4q^{7} + 4q^{11} - q^{13} + 6q^{17} + O(q^{20})\)  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.