Properties

Label 287490.m
Number of curves $6$
Conductor $287490$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("287490.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 287490.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
287490.m1 287490m6 [1, 1, 0, -22999228, -42463524422] [2] 13271040  
287490.m2 287490m4 [1, 1, 0, -1437478, -663915872] [2, 2] 6635520  
287490.m3 287490m5 [1, 1, 0, -1341648, -756123498] [2] 13271040  
287490.m4 287490m3 [1, 1, 0, -506558, 130947432] [2] 6635520  
287490.m5 287490m2 [1, 1, 0, -95858, -8936988] [2, 2] 3317760  
287490.m6 287490m1 [1, 1, 0, 13662, -854412] [2] 1658880 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 287490.m have rank \(0\).

Modular form 287490.2.a.m

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} + 2q^{13} - q^{14} + q^{15} + q^{16} - 2q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.