Properties

Label 252.b
Number of curves 4
Conductor 252
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("252.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 252.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
252.b1 252a4 [0, 0, 0, -16455, 812446] [6] 288  
252.b2 252a3 [0, 0, 0, -1020, 12913] [6] 144  
252.b3 252a2 [0, 0, 0, -255, 502] [2] 96  
252.b4 252a1 [0, 0, 0, 60, 61] [2] 48 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 252.b have rank \(0\).

Modular form 252.2.a.b

sage: E.q_eigenform(10)
 
\( q + q^{7} + 6q^{11} + 2q^{13} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.