Properties

Label 46475.b
Number of curves 3
Conductor 46475
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("46475.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46475.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46475.b1 46475a3 [0, 1, 1, -33040908, -73112478656] [] 1512000  
46475.b2 46475a2 [0, 1, 1, -43658, -6374156] [] 302400  
46475.b3 46475a1 [0, 1, 1, -1408, 47844] [] 60480 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46475.b have rank \(1\).

Modular form 46475.2.a.b

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

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.