Properties

Label 160113.i
Number of curves $1$
Conductor $160113$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 160113.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160113.i1 160113f1 \([0, 1, 1, -6554, 222509]\) \(-1404928/171\) \(-3790105753059\) \([]\) \(585728\) \(1.1486\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 160113.i1 has rank \(1\).

Complex multiplication

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

Modular form 160113.2.a.i

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