Properties

Label 72450be
Number of curves $4$
Conductor $72450$
CM no
Rank $1$
Graph

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

Elliptic curves in class 72450be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
72450.r3 72450be1 [1, -1, 0, -28602792, -63053576384] [2] 8847360 \(\Gamma_0(N)\)-optimal
72450.r2 72450be2 [1, -1, 0, -466614792, -3879452132384] [2] 17694720  
72450.r4 72450be3 [1, -1, 0, 169573833, -2374036259] [2] 26542080  
72450.r1 72450be4 [1, -1, 0, -678298167, -18483604259] [2] 53084160  

Rank

sage: E.rank()
 

The elliptic curves in class 72450be have rank \(1\).

Complex multiplication

The elliptic curves in class 72450be do not have complex multiplication.

Modular form 72450.2.a.be

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{7} - q^{8} + 4q^{13} + q^{14} + q^{16} + 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.