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Properties

Label 24882p
Number of curves $2$
Conductor $24882$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 24882p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24882.q2 24882p1 \([1, 0, 1, 37569, 1608850]\) \(5864476297107620375/4507634865896448\) \(-4507634865896448\) \([2]\) \(138240\) \(1.6918\) \(\Gamma_0(N)\)-optimal
24882.q1 24882p2 \([1, 0, 1, -175391, 13790162]\) \(596680802837154843625/262974330114189408\) \(262974330114189408\) \([2]\) \(276480\) \(2.0384\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24882p have rank \(0\).

Complex multiplication

The elliptic curves in class 24882p do not have complex multiplication.

Modular form 24882.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{11} + q^{12} - q^{13} + q^{16} - 2 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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.