Properties

Label 209484.k
Number of curves $1$
Conductor $209484$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 209484.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
209484.k1 209484g1 \([0, 0, 0, -2067861, 106065029]\) \(299591084078848/171885556953\) \(561045703335270093072\) \([]\) \(6815232\) \(2.6710\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 209484.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 209484.k do not have complex multiplication.

Modular form 209484.2.a.k

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