Properties

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

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

Elliptic curves in class 430950ix

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
430950.ix4 430950ix1 \([1, 0, 0, 6675412, 1126203792]\) \(436192097814719/259683840000\) \(-19585067126040000000000\) \([2]\) \(46448640\) \(2.9667\) \(\Gamma_0(N)\)-optimal*
430950.ix3 430950ix2 \([1, 0, 0, -27124588, 9069203792]\) \(29263955267177281/16463793153600\) \(1241681015123982225000000\) \([2, 2]\) \(92897280\) \(3.3133\) \(\Gamma_0(N)\)-optimal*
430950.ix1 430950ix3 \([1, 0, 0, -323719588, 2237980628792]\) \(49745123032831462081/97939634471640\) \(7386498580069096824375000\) \([2]\) \(185794560\) \(3.6599\) \(\Gamma_0(N)\)-optimal*
430950.ix2 430950ix4 \([1, 0, 0, -271329588, -1711355021208]\) \(29291056630578924481/175463302795560\) \(13233247642239596375625000\) \([2]\) \(185794560\) \(3.6599\)  
*optimality has not been determined 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 \(0\).

Complex multiplication

The elliptic curves in class 430950ix do not have complex multiplication.

Modular form 430950.2.a.ix

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

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.