Properties

Label 338130s
Number of curves $2$
Conductor $338130$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 338130s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
338130.s2 338130s1 [1, -1, 0, -236745, -9569219] [2] 4456448 \(\Gamma_0(N)\)-optimal
338130.s1 338130s2 [1, -1, 0, -2889765, -1887376775] [2] 8912896  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 338130.2.a.s

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + 4q^{11} + q^{13} + q^{16} + 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.