Properties

Label 112530.be
Number of curves $6$
Conductor $112530$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("112530.be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 112530.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
112530.be1 112530bd6 [1, 0, 1, -37209923, 87361653938] [2] 5242880  
112530.be2 112530bd4 [1, 0, 1, -2325623, 1364877578] [2, 2] 2621440  
112530.be3 112530bd5 [1, 0, 1, -2289323, 1409555618] [2] 5242880  
112530.be4 112530bd3 [1, 0, 1, -447703, -89933494] [2] 2621440  
112530.be5 112530bd2 [1, 0, 1, -147623, 20615978] [2, 2] 1310720  
112530.be6 112530bd1 [1, 0, 1, 7257, 1348906] [2] 655360 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 112530.be have rank \(2\).

Modular form 112530.2.a.be

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} + q^{12} - 6q^{13} + q^{15} + q^{16} - 2q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.