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Properties

Label 24990.bg
Number of curves $2$
Conductor $24990$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 24990.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24990.bg1 24990be2 \([1, 0, 1, -129533, 10900586]\) \(5956317014383/2172381210\) \(87663417602524470\) \([2]\) \(258048\) \(1.9514\)  
24990.bg2 24990be1 \([1, 0, 1, 24817, 1207406]\) \(41890384817/39795300\) \(-1605883896647100\) \([2]\) \(129024\) \(1.6048\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 24990.bg have rank \(0\).

Complex multiplication

The elliptic curves in class 24990.bg do not have complex multiplication.

Modular form 24990.2.a.bg

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.