Properties

Label 338130bp
Number of curves $6$
Conductor $338130$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("338130.bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 338130bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
338130.bp6 338130bp1 [1, -1, 0, 38961, -1195155] [2] 2359296 \(\Gamma_0(N)\)-optimal
338130.bp5 338130bp2 [1, -1, 0, -169119, -9809667] [2, 2] 4718592  
338130.bp3 338130bp3 [1, -1, 0, -1469619, 679195233] [2, 2] 9437184  
338130.bp2 338130bp4 [1, -1, 0, -2197899, -1252640295] [2] 9437184  
338130.bp1 338130bp5 [1, -1, 0, -23448069, 43708604643] [2] 18874368  
338130.bp4 338130bp6 [1, -1, 0, -299169, 1730493423] [2] 18874368  

Rank

sage: E.rank()
 

The elliptic curves in class 338130bp have rank \(0\).

Modular form 338130.2.a.bp

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.