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Properties

Label 59290cb
Number of curves $2$
Conductor $59290$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 59290cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59290.bz2 59290cb1 \([1, 1, 0, -421082, 123507476]\) \(-115501303/25600\) \(-1830115235085491200\) \([2]\) \(1433600\) \(2.2247\) \(\Gamma_0(N)\)-optimal
59290.bz1 59290cb2 \([1, 1, 0, -7061562, 7219524404]\) \(544737993463/20000\) \(1429777527410540000\) \([2]\) \(2867200\) \(2.5713\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 59290.2.a.cb

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.