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Properties

Label 160113.b
Number of curves $2$
Conductor $160113$
CM no
Rank $0$
Graph

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

Elliptic curves in class 160113.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160113.b1 160113b1 \([1, 1, 1, -220565, -30493654]\) \(53540005609/12969153\) \(287452990629253737\) \([2]\) \(2021760\) \(2.0609\) \(\Gamma_0(N)\)-optimal
160113.b2 160113b2 \([1, 1, 1, 523820, -191280814]\) \(717157709351/1129784517\) \(-25040952032740839693\) \([2]\) \(4043520\) \(2.4075\)  

Rank

sage: E.rank()
 

The elliptic curves in class 160113.b have rank \(0\).

Complex multiplication

The elliptic curves in class 160113.b do not have complex multiplication.

Modular form 160113.2.a.b

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