Properties

Label 82810.n
Number of curves $2$
Conductor $82810$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 82810.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82810.n1 82810bf1 \([1, 1, 0, -82390153472, -9102542581769216]\) \(-644487634439863642624729/896000\) \(-85989033621056384000\) \([]\) \(129392640\) \(4.4743\) \(\Gamma_0(N)\)-optimal
82810.n2 82810bf2 \([1, 1, 0, -82368084607, -9107662613459899]\) \(-643969879566315506524489/719323136000000000\) \(-69033372015522001977344000000000\) \([]\) \(388177920\) \(5.0236\)  

Rank

sage: E.rank()
 

The elliptic curves in class 82810.n have rank \(1\).

Complex multiplication

The elliptic curves in class 82810.n do not have complex multiplication.

Modular form 82810.2.a.n

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