Properties

Label 430950ep
Number of curves 8
Conductor 430950
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("430950.ep1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 430950ep

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
430950.ep7 430950ep1 [1, 1, 1, -8856216938, 308890597831031] [u'2'] 1114767360 \(\Gamma_0(N)\)-optimal
430950.ep6 430950ep2 [1, 1, 1, -23479448938, -974034791992969] [u'2', u'2'] 2229534720  
430950.ep5 430950ep3 [1, 1, 1, -108974520938, -13756221892792969] [u'2'] 3344302080  
430950.ep8 430950ep4 [1, 1, 1, 62871439062, -6473895550488969] [u'2'] 4459069440  
430950.ep4 430950ep5 [1, 1, 1, -343802048938, -77581106517592969] [u'2'] 4459069440  
430950.ep2 430950ep6 [1, 1, 1, -1740435962938, -883762402145248969] [u'2', u'2'] 6688604160  
430950.ep3 430950ep7 [1, 1, 1, -1737279972438, -887127155104842969] [u'2'] 13377208320  
430950.ep1 430950ep8 [1, 1, 1, -27846975025438, -56560760556113998969L] [u'2'] 13377208320  

Rank

sage: E.rank()
 

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

Modular form 430950.2.a.ep

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.