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Properties

Label 10829.a
Number of curves $2$
Conductor $10829$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 10829.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10829.a1 10829c2 \([1, -1, 1, -574167, -167314150]\) \(177930109857804849/634933\) \(74699232517\) \([2]\) \(86400\) \(1.7281\)  
10829.a2 10829c1 \([1, -1, 1, -35902, -2605060]\) \(43499078731809/82055753\) \(9653777284697\) \([2]\) \(43200\) \(1.3816\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10829.a have rank \(1\).

Complex multiplication

The elliptic curves in class 10829.a do not have complex multiplication.

Modular form 10829.2.a.a

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