Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 24882.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24882.u1 24882u1 \([1, 0, 1, -397, 3968]\) \(-6894801108937/2926421784\) \(-2926421784\) \([3]\) \(15552\) \(0.52416\) \(\Gamma_0(N)\)-optimal
24882.u2 24882u2 \([1, 0, 1, 3068, -44542]\) \(3195164697368903/2715996501504\) \(-2715996501504\) \([]\) \(46656\) \(1.0735\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 24882.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - 3 q^{10} + q^{11} + q^{12} + q^{13} + q^{14} + 3 q^{15} + q^{16} - 3 q^{17} - q^{18} + 5 q^{19} + O(q^{20})\) 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.