Properties

Label 101430co
Number of curves $6$
Conductor $101430$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("101430.bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 101430co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
101430.bp5 101430co1 [1, -1, 0, -185229, 33710053] [2] 1179648 \(\Gamma_0(N)\)-optimal
101430.bp4 101430co2 [1, -1, 0, -3042909, 2043802165] [2, 2] 2359296  
101430.bp3 101430co3 [1, -1, 0, -3122289, 1931606473] [2, 2] 4718592  
101430.bp1 101430co4 [1, -1, 0, -48686409, 130767600865] [2] 4718592  
101430.bp6 101430co5 [1, -1, 0, 3876381, 9354395875] [2] 9437184  
101430.bp2 101430co6 [1, -1, 0, -11391039, -12672659777] [2] 9437184  

Rank

sage: E.rank()
 

The elliptic curves in class 101430co have rank \(1\).

Modular form 101430.2.a.bp

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 4q^{11} + 2q^{13} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.