Properties

Label 76664b
Number of curves $4$
Conductor $76664$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76664b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76664.b4 76664b1 [0, 0, 0, 1369, 101306] [2] 103680 \(\Gamma_0(N)\)-optimal
76664.b3 76664b2 [0, 0, 0, -26011, 1519590] [2, 2] 207360  
76664.b2 76664b3 [0, 0, 0, -80771, -6990114] [2] 414720  
76664.b1 76664b4 [0, 0, 0, -409331, 100799470] [2] 414720  

Rank

sage: E.rank()
 

The elliptic curves in class 76664b have rank \(1\).

Complex multiplication

The elliptic curves in class 76664b do not have complex multiplication.

Modular form 76664.2.a.b

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.