Properties

Label 38115k
Number of curves 4
Conductor 38115
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("38115.v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38115k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38115.v3 38115k1 [1, -1, 0, -2745, 53136] [2] 46080 \(\Gamma_0(N)\)-optimal
38115.v2 38115k2 [1, -1, 0, -8190, -218025] [2, 2] 92160  
38115.v4 38115k3 [1, -1, 0, 19035, -1377810] [2] 184320  
38115.v1 38115k4 [1, -1, 0, -122535, -16477884] [2] 184320  

Rank

sage: E.rank()
 

The elliptic curves in class 38115k have rank \(1\).

Modular form 38115.2.a.v

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.