Properties

Label 6776.g
Number of curves $4$
Conductor $6776$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6776.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6776.g1 6776c3 [0, 0, 0, -36179, -2648690] [2] 10240  
6776.g2 6776c4 [0, 0, 0, -7139, 183678] [2] 10240  
6776.g3 6776c2 [0, 0, 0, -2299, -39930] [2, 2] 5120  
6776.g4 6776c1 [0, 0, 0, 121, -2662] [2] 2560 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6776.g have rank \(1\).

Complex multiplication

The elliptic curves in class 6776.g do not have complex multiplication.

Modular form 6776.2.a.g

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.