Properties

Label 11858.bm
Number of curves 6
Conductor 11858
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("11858.bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11858.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11858.bm1 11858bk6 [1, 1, 1, -16189258, -25078719401] [2] 414720  
11858.bm2 11858bk5 [1, 1, 1, -1011018, -392829865] [2] 207360  
11858.bm3 11858bk4 [1, 1, 1, -210603, -30579823] [2] 138240  
11858.bm4 11858bk2 [1, 1, 1, -62378, 5966533] [2] 46080  
11858.bm5 11858bk1 [1, 1, 1, -3088, 132397] [2] 23040 \(\Gamma_0(N)\)-optimal
11858.bm6 11858bk3 [1, 1, 1, 26557, -2784671] [2] 69120  

Rank

sage: E.rank()
 

The elliptic curves in class 11858.bm have rank \(0\).

Modular form 11858.2.a.bm

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.