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Properties

Label 59290u
Number of curves $2$
Conductor $59290$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 59290u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59290.k1 59290u1 \([1, 1, 0, -830183, -843257477]\) \(-2509090441/10718750\) \(-270317313776055218750\) \([]\) \(2737152\) \(2.6056\) \(\Gamma_0(N)\)-optimal
59290.k2 59290u2 \([1, 1, 0, 7322192, 20325199448]\) \(1721540467559/8070721400\) \(-203536394550010370756600\) \([]\) \(8211456\) \(3.1549\)  

Rank

sage: E.rank()
 

The elliptic curves in class 59290u have rank \(1\).

Complex multiplication

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

Modular form 59290.2.a.u

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