Properties

Label 169065.e
Number of curves $1$
Conductor $169065$
CM no
Rank $2$

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

Elliptic curves in class 169065.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169065.e1 169065a1 \([0, 0, 1, -123267, 16658032]\) \(-57834888040448/823875\) \(-2950771750875\) \([]\) \(1188864\) \(1.5324\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 169065.e1 has rank \(2\).

Complex multiplication

The elliptic curves in class 169065.e do not have complex multiplication.

Modular form 169065.2.a.e

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