Properties

Label 59290by
Number of curves $2$
Conductor $59290$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 59290by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59290.x1 59290by1 \([1, 1, 0, -2525877, 1547279749]\) \(-584043889/1400\) \(-4272116893636268600\) \([]\) \(1824768\) \(2.4543\) \(\Gamma_0(N)\)-optimal
59290.x2 59290by2 \([1, 1, 0, 4648213, 7801651411]\) \(3639707951/10718750\) \(-32708394966902681468750\) \([]\) \(5474304\) \(3.0036\)  

Rank

sage: E.rank()
 

The elliptic curves in class 59290by have rank \(0\).

Complex multiplication

The elliptic curves in class 59290by do not have complex multiplication.

Modular form 59290.2.a.by

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.