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Properties

Label 116281b
Number of curves $2$
Conductor $116281$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116281b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
116281.c2 116281b1 [1, 0, 1, -2423, 179199] [] 183600 \(\Gamma_0(N)\)-optimal
116281.c1 116281b2 [1, 0, 1, -3490853, -2510792715] [] 2019600  

Rank

sage: E.rank()
 

The elliptic curves in class 116281b have rank \(1\).

Complex multiplication

The elliptic curves in class 116281b do not have complex multiplication.

Modular form 116281.2.a.b

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

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.