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Properties

Label 59290.db
Number of curves $2$
Conductor $59290$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("db1")
 
E.isogeny_class()
 

Elliptic curves in class 59290.db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59290.db1 59290em1 \([1, 1, 1, -20875, -1171983]\) \(-584043889/1400\) \(-2411498612600\) \([]\) \(165888\) \(1.2553\) \(\Gamma_0(N)\)-optimal
59290.db2 59290em2 \([1, 1, 1, 38415, -5844035]\) \(3639707951/10718750\) \(-18463036252718750\) \([]\) \(497664\) \(1.8046\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 59290.2.a.db

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 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.