Properties

Label 201810a
Number of curves $6$
Conductor $201810$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("201810.cr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 201810a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
201810.cr6 201810a1 [1, 0, 0, 9590, 506660] [2] 921600 \(\Gamma_0(N)\)-optimal
201810.cr5 201810a2 [1, 0, 0, -67290, 5227092] [2, 2] 1843200  
201810.cr2 201810a3 [1, 0, 0, -1009070, 390038400] [2, 2] 3686400  
201810.cr4 201810a4 [1, 0, 0, -355590, -77169048] [2] 3686400  
201810.cr1 201810a5 [1, 0, 0, -16144820, 24967469250] [2] 7372800  
201810.cr3 201810a6 [1, 0, 0, -941800, 444298382] [2] 7372800  

Rank

sage: E.rank()
 

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

Modular form 201810.2.a.cr

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.