Properties

Label 430950ix
Number of curves 4
Conductor 430950
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("430950.ix1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 430950ix

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
430950.ix4 430950ix1 [1, 0, 0, 6675412, 1126203792] [2] 46448640 \(\Gamma_0(N)\)-optimal*
430950.ix3 430950ix2 [1, 0, 0, -27124588, 9069203792] [2, 2] 92897280 \(\Gamma_0(N)\)-optimal*
430950.ix1 430950ix3 [1, 0, 0, -323719588, 2237980628792] [2] 185794560 \(\Gamma_0(N)\)-optimal*
430950.ix2 430950ix4 [1, 0, 0, -271329588, -1711355021208] [2] 185794560  
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 430950ix1.

Rank

sage: E.rank()
 

The elliptic curves in class 430950ix have rank \(0\).

Modular form 430950.2.a.ix

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} + 4q^{7} + q^{8} + q^{9} + 4q^{11} + q^{12} + 4q^{14} + q^{16} + q^{17} + q^{18} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.