Properties

Label 59584co
Number of curves $3$
Conductor $59584$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 59584co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59584.db3 59584co1 \([0, -1, 0, 131, -69]\) \(32768/19\) \(-143061184\) \([]\) \(18144\) \(0.25436\) \(\Gamma_0(N)\)-optimal
59584.db2 59584co2 \([0, -1, 0, -1829, -31429]\) \(-89915392/6859\) \(-51645087424\) \([]\) \(54432\) \(0.80366\)  
59584.db1 59584co3 \([0, -1, 0, -150789, -22487149]\) \(-50357871050752/19\) \(-143061184\) \([]\) \(163296\) \(1.3530\)  

Rank

sage: E.rank()
 

The elliptic curves in class 59584co have rank \(1\).

Complex multiplication

The elliptic curves in class 59584co do not have complex multiplication.

Modular form 59584.2.a.co

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