Properties

Label 38115m
Number of curves $6$
Conductor $38115$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38115m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38115.h6 38115m1 [1, -1, 1, 38092, -831265234] [2] 921600 \(\Gamma_0(N)\)-optimal
38115.h5 38115m2 [1, -1, 1, -13035353, -17790138088] [2, 2] 1843200  
38115.h4 38115m3 [1, -1, 1, -27709628, 29613639872] [2] 3686400  
38115.h2 38115m4 [1, -1, 1, -207536198, -1150718660044] [2, 2] 3686400  
38115.h3 38115m5 [1, -1, 1, -206507093, -1162696207318] [2] 7372800  
38115.h1 38115m6 [1, -1, 1, -3320578823, -73648500528094] [2] 7372800  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 38115m do not have complex multiplication.

Modular form 38115.2.a.m

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.