Properties

Label 338130j
Number of curves $4$
Conductor $338130$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 338130j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
338130.j3 338130j1 [1, -1, 0, -15660, -4838000] [2] 1990656 \(\Gamma_0(N)\)-optimal
338130.j2 338130j2 [1, -1, 0, -535860, -150181880] [2] 3981312  
338130.j4 338130j3 [1, -1, 0, 140400, 127906636] [2] 5971968  
338130.j1 338130j4 [1, -1, 0, -3110850, 2005178386] [2] 11943936  

Rank

sage: E.rank()
 

The elliptic curves in class 338130j have rank \(1\).

Complex multiplication

The elliptic curves in class 338130j do not have complex multiplication.

Modular form 338130.2.a.j

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.