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Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 59290.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59290.u1 59290bv1 \([1, 1, 0, -243212, -78434264]\) \(-63088729/68600\) \(-1730030808166753400\) \([]\) \(912384\) \(2.1944\) \(\Gamma_0(N)\)-optimal
59290.u2 59290bv2 \([1, 1, 0, 2039453, 1419450509]\) \(37199299511/56000000\) \(-1412270047483064000000\) \([]\) \(2737152\) \(2.7437\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 59290.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} - 2 q^{9} - q^{10} - q^{12} + q^{13} - q^{15} + q^{16} - 6 q^{17} + 2 q^{18} + 7 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.