Properties

Label 666.e
Number of curves $1$
Conductor $666$
CM no
Rank $1$

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

Elliptic curves in class 666.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
666.e1 666d1 \([1, -1, 1, -26, 57]\) \(-69426531/1184\) \(-31968\) \([]\) \(80\) \(-0.33719\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 666.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 666.e do not have complex multiplication.

Modular form 666.2.a.e

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