Properties

Label 45486p
Number of curves 6
Conductor 45486
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("45486.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 45486p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
45486.m5 45486p1 [1, -1, 0, -1692, 54652] [2] 57024 \(\Gamma_0(N)\)-optimal
45486.m4 45486p2 [1, -1, 0, -34182, 2439418] [2] 114048  
45486.m6 45486p3 [1, -1, 0, 14553, -1137731] [2] 171072  
45486.m3 45486p4 [1, -1, 0, -115407, -12340283] [2] 342144  
45486.m2 45486p5 [1, -1, 0, -554022, -159042380] [2] 513216  
45486.m1 45486p6 [1, -1, 0, -8871462, -10168249676] [2] 1026432  

Rank

sage: E.rank()
 

The elliptic curves in class 45486p have rank \(0\).

Modular form 45486.2.a.m

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{7} - q^{8} + 4q^{13} - q^{14} + q^{16} - 6q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.