Properties

Label 201810bb
Number of curves 8
Conductor 201810
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("201810.ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 201810bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
201810.ca7 201810bb1 [1, 1, 1, 201790, -26206513] [2] 3932160 \(\Gamma_0(N)\)-optimal
201810.ca6 201810bb2 [1, 1, 1, -1028290, -235812145] [2, 2] 7864320  
201810.ca5 201810bb3 [1, 1, 1, -7255570, 7351505807] [2, 2] 15728640  
201810.ca4 201810bb4 [1, 1, 1, -14482290, -21213288945] [2] 15728640  
201810.ca2 201810bb5 [1, 1, 1, -115368070, 476905715807] [2, 2] 31457280  
201810.ca8 201810bb6 [1, 1, 1, 1220450, 23510190335] [2] 31457280  
201810.ca1 201810bb7 [1, 1, 1, -1845888820, 30524283602207] [2] 62914560  
201810.ca3 201810bb8 [1, 1, 1, -114647320, 483159519407] [2] 62914560  

Rank

sage: E.rank()
 

The elliptic curves in class 201810bb have rank \(0\).

Modular form 201810.2.a.ca

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} + 2q^{13} - q^{14} - q^{15} + q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.