Properties

Label 172480.be
Number of curves 4
Conductor 172480
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("172480.be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 172480.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
172480.be1 172480ed4 [0, 1, 0, -1391665, 631438863] [2] 1990656  
172480.be2 172480ed3 [0, 1, 0, -87285, 9771355] [2] 995328  
172480.be3 172480ed2 [0, 1, 0, -19665, 593263] [2] 663552  
172480.be4 172480ed1 [0, 1, 0, -8885, -318725] [2] 331776 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 172480.be have rank \(2\).

Modular form 172480.2.a.be

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} + q^{9} + q^{11} - 4q^{13} - 2q^{15} - 4q^{19} + O(q^{20}) \)

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.