Properties

Label 5776q
Number of curves $3$
Conductor $5776$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5776q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5776.c3 5776q1 \([0, 1, 0, 3851, -2781]\) \(32768/19\) \(-3661298642944\) \([]\) \(8640\) \(1.1002\) \(\Gamma_0(N)\)-optimal
5776.c2 5776q2 \([0, 1, 0, -53909, -5143421]\) \(-89915392/6859\) \(-1321728810102784\) \([]\) \(25920\) \(1.6495\)  
5776.c1 5776q3 \([0, 1, 0, -4443669, -3606941501]\) \(-50357871050752/19\) \(-3661298642944\) \([]\) \(77760\) \(2.1988\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5776q have rank \(1\).

Complex multiplication

The elliptic curves in class 5776q do not have complex multiplication.

Modular form 5776.2.a.q

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + 3q^{5} + q^{7} + q^{9} - 3q^{11} + 4q^{13} - 6q^{15} - 3q^{17} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.