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Properties

Label 80850bg
Number of curves $2$
Conductor $80850$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 80850bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80850.c2 80850bg1 \([1, 1, 0, 2519800, 252121500]\) \(16035452615/9526572\) \(-1051179999147042187500\) \([]\) \(5443200\) \(2.7230\) \(\Gamma_0(N)\)-optimal
80850.c1 80850bg2 \([1, 1, 0, -37997075, 94372822125]\) \(-54983678740585/3061257408\) \(-337784940850740075000000\) \([]\) \(16329600\) \(3.2723\)  

Rank

sage: E.rank()
 

The elliptic curves in class 80850bg have rank \(1\).

Complex multiplication

The elliptic curves in class 80850bg do not have complex multiplication.

Modular form 80850.2.a.bg

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