Properties

Label 18150.d
Number of curves 8
Conductor 18150
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("18150.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18150.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18150.d1 18150m8 [1, 1, 0, -16133900, 24936765000] [2] 829440  
18150.d2 18150m7 [1, 1, 0, -1371900, 83607000] [2] 829440  
18150.d3 18150m6 [1, 1, 0, -1008900, 388890000] [2, 2] 414720  
18150.d4 18150m4 [1, 1, 0, -872775, -314195625] [2] 276480  
18150.d5 18150m5 [1, 1, 0, -207275, 31198875] [2] 276480  
18150.d6 18150m2 [1, 1, 0, -56025, -4647375] [2, 2] 138240  
18150.d7 18150m3 [1, 1, 0, -40900, 10402000] [2] 207360  
18150.d8 18150m1 [1, 1, 0, 4475, -351875] [2] 69120 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 18150.d have rank \(0\).

Modular form 18150.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} - 4q^{7} - q^{8} + q^{9} - q^{12} + 2q^{13} + 4q^{14} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.