Properties

Label 84966.dr
Number of curves 6
Conductor 84966
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("84966.dr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 84966.dr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
84966.dr1 84966dv6 [1, 0, 0, -392883079, 2997356200775] [2] 14155776  
84966.dr2 84966dv4 [1, 0, 0, -24555469, 46831048109] [2, 2] 7077888  
84966.dr3 84966dv5 [1, 0, 0, -23280979, 51909380963] [2] 14155776  
84966.dr4 84966dv2 [1, 0, 0, -1614649, 651177449] [2, 2] 3538944  
84966.dr5 84966dv1 [1, 0, 0, -481769, -119407527] [2] 1769472 \(\Gamma_0(N)\)-optimal
84966.dr6 84966dv3 [1, 0, 0, 3200091, 3793276773] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 84966.dr have rank \(0\).

Modular form 84966.2.a.dr

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.