Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.q1 46800y4 \([0, 0, 0, -372675, -87236750]\) \(490757540836/2142075\) \(24985162800000000\) \([2]\) \(589824\) \(1.9993\)  
46800.q2 46800y2 \([0, 0, 0, -35175, 175750]\) \(1650587344/950625\) \(2772022500000000\) \([2, 2]\) \(294912\) \(1.6528\)  
46800.q3 46800y1 \([0, 0, 0, -25050, 1522375]\) \(9538484224/26325\) \(4797731250000\) \([2]\) \(147456\) \(1.3062\) \(\Gamma_0(N)\)-optimal
46800.q4 46800y3 \([0, 0, 0, 140325, 1404250]\) \(26198797244/15234375\) \(-177693750000000000\) \([2]\) \(589824\) \(1.9993\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 46800.2.a.q

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 LMFDB 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 LMFDB labels.