Properties

Label 162624dm
Number of curves 6
Conductor 162624
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("162624.do1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162624dm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162624.do4 162624dm1 [0, -1, 0, -263457, 52120257] [2] 1228800 \(\Gamma_0(N)\)-optimal
162624.do3 162624dm2 [0, -1, 0, -302177, 35834625] [2, 2] 2457600  
162624.do6 162624dm3 [0, -1, 0, 975583, 258420417] [2] 4915200  
162624.do2 162624dm4 [0, -1, 0, -2199457, -1229651135] [2, 2] 4915200  
162624.do5 162624dm5 [0, -1, 0, 239903, -3810006143] [2] 9830400  
162624.do1 162624dm6 [0, -1, 0, -34995297, -79670741247] [2] 9830400  

Rank

sage: E.rank()
 

The elliptic curves in class 162624dm have rank \(0\).

Modular form 162624.2.a.do

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{5} + q^{7} + q^{9} + 6q^{13} - 2q^{15} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.