Properties

Label 77658.t
Number of curves $6$
Conductor $77658$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("77658.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 77658.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
77658.t1 77658t4 [1, 0, 1, -2485095, -1508072162] [2] 1290240  
77658.t2 77658t6 [1, 0, 1, -1690025, 837384338] [2] 2580480  
77658.t3 77658t3 [1, 0, 1, -192335, -11506354] [2, 2] 1290240  
77658.t4 77658t2 [1, 0, 1, -155355, -23561834] [2, 2] 645120  
77658.t5 77658t1 [1, 0, 1, -7435, -545482] [2] 322560 \(\Gamma_0(N)\)-optimal
77658.t6 77658t5 [1, 0, 1, 713675, -88698406] [2] 2580480  

Rank

sage: E.rank()
 

The elliptic curves in class 77658.t have rank \(0\).

Modular form 77658.2.a.t

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.