Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 160113.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160113.e1 160113e1 \([1, 0, 1, -872211413, -9914800356025]\) \(-1178642372740721641/90876411\) \(-5657937214555601305371\) \([]\) \(44715888\) \(3.6216\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 160113.e1 has rank \(1\).

Complex multiplication

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

Modular form 160113.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 3 q^{7} - 3 q^{8} + q^{9} + q^{10} + 5 q^{11} - q^{12} - 4 q^{13} - 3 q^{14} + q^{15} - q^{16} - 2 q^{17} + q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display