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Properties

Label 82110.bv
Number of curves $2$
Conductor $82110$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bv1")
 
E.isogeny_class()
 

Elliptic curves in class 82110.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82110.bv1 82110bv2 \([1, 0, 0, -29285, -1930815]\) \(2777540013143436241/925168184640\) \(925168184640\) \([2]\) \(245760\) \(1.2689\)  
82110.bv2 82110bv1 \([1, 0, 0, -2085, -21375]\) \(1002431968831441/385930137600\) \(385930137600\) \([2]\) \(122880\) \(0.92231\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 82110.bv have rank \(1\).

Complex multiplication

The elliptic curves in class 82110.bv do not have complex multiplication.

Modular form 82110.2.a.bv

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.