Properties

Label 2299.b
Number of curves $3$
Conductor $2299$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2299.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2299.b1 2299d3 \([0, 1, 1, -93089, 10900929]\) \(-50357871050752/19\) \(-33659659\) \([]\) \(4050\) \(1.2324\)  
2299.b2 2299d2 \([0, 1, 1, -1129, 15164]\) \(-89915392/6859\) \(-12151136899\) \([]\) \(1350\) \(0.68308\)  
2299.b3 2299d1 \([0, 1, 1, 81, 39]\) \(32768/19\) \(-33659659\) \([]\) \(450\) \(0.13377\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2299.b have rank \(0\).

Complex multiplication

The elliptic curves in class 2299.b do not have complex multiplication.

Modular form 2299.2.a.b

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.