Properties

Label 116.b
Number of curves $2$
Conductor $116$
CM no
Rank $0$
Graph

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

Elliptic curves in class 116.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116.b1 116b1 \([0, 1, 0, -4, 4]\) \(-35152/29\) \(-7424\) \([3]\) \(8\) \(-0.55932\) \(\Gamma_0(N)\)-optimal
116.b2 116b2 \([0, 1, 0, 36, -76]\) \(19600688/24389\) \(-6243584\) \([]\) \(24\) \(-0.010013\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116.b have rank \(0\).

Complex multiplication

The elliptic curves in class 116.b do not have complex multiplication.

Modular form 116.2.a.b

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