Properties

Label 166410ca
Number of curves $1$
Conductor $166410$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 166410ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166410.c1 166410ca1 \([1, -1, 0, 84311280, -10260091007744]\) \(14382768678616871/9876709319915520\) \(-45514579433317730300693329920\) \([]\) \(156119040\) \(4.1780\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 166410ca1 has rank \(1\).

Complex multiplication

The elliptic curves in class 166410ca do not have complex multiplication.

Modular form 166410.2.a.ca

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