Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 338130e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
338130.e1 338130e1 [1, -1, 0, -46005, -1692235] [2] 2359296 \(\Gamma_0(N)\)-optimal
338130.e2 338130e2 [1, -1, 0, 162075, -12886939] [2] 4718592  

Rank

sage: E.rank()
 

The elliptic curves in class 338130e have rank \(2\).

Complex multiplication

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

Modular form 338130.2.a.e

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - 2q^{7} - q^{8} + q^{10} - 4q^{11} - q^{13} + 2q^{14} + q^{16} - 6q^{19} + O(q^{20}) \)

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.