Properties

Label 38115.k
Number of curves $6$
Conductor $38115$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("38115.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38115.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38115.k1 38115s6 [1, -1, 1, -14429273, -21092093778] [2] 1966080  
38115.k2 38115s4 [1, -1, 1, -952898, -289961328] [2, 2] 983040  
38115.k3 38115s2 [1, -1, 1, -294053, 57381756] [2, 2] 491520  
38115.k4 38115s1 [1, -1, 1, -288608, 59749242] [2] 245760 \(\Gamma_0(N)\)-optimal
38115.k5 38115s3 [1, -1, 1, 277672, 253140396] [2] 983040  
38115.k6 38115s5 [1, -1, 1, 1981957, -1725692394] [2] 1966080  

Rank

sage: E.rank()
 

The elliptic curves in class 38115.k have rank \(0\).

Modular form 38115.2.a.k

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.