Properties

Label 77616.dq
Number of curves 4
Conductor 77616
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("77616.dq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 77616.dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
77616.dq1 77616ex3 [0, 0, 0, -568155, 164203018] [2] 829440  
77616.dq2 77616ex4 [0, 0, 0, -285915, 327394186] [2] 1658880  
77616.dq3 77616ex1 [0, 0, 0, -38955, -2791334] [2] 276480 \(\Gamma_0(N)\)-optimal
77616.dq4 77616ex2 [0, 0, 0, 31605, -11780678] [2] 552960  

Rank

sage: E.rank()
 

The elliptic curves in class 77616.dq have rank \(0\).

Modular form 77616.2.a.dq

sage: E.q_eigenform(10)
 
\( q - q^{11} + 4q^{13} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.