Properties

Label 50430.f
Number of curves 8
Conductor 50430
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("50430.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 50430.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
50430.f1 50430f7 [1, 1, 0, -8965648, -10336598792] [2] 1658880  
50430.f2 50430f8 [1, 1, 0, -762368, -35188728] [2] 1658880  
50430.f3 50430f6 [1, 1, 0, -560648, -161505792] [2, 2] 829440  
50430.f4 50430f5 [1, 1, 0, -485003, 129803103] [2] 552960  
50430.f5 50430f4 [1, 1, 0, -115183, -13007933] [2] 552960  
50430.f6 50430f2 [1, 1, 0, -31133, 1902537] [2, 2] 276480  
50430.f7 50430f3 [1, 1, 0, -22728, -4325568] [2] 414720  
50430.f8 50430f1 [1, 1, 0, 2487, 147573] [2] 138240 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 50430.f have rank \(1\).

Modular form 50430.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 4q^{7} - q^{8} + q^{9} + q^{10} - q^{12} - 2q^{13} - 4q^{14} + q^{15} + q^{16} - 6q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.