Properties

Label 194398k
Number of curves $1$
Conductor $194398$
CM no
Rank $1$

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

Elliptic curves in class 194398k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
194398.s1 194398k1 \([1, -1, 1, -3595251, 2613958867]\) \(2003092024307193/9529458688\) \(24449983819276091392\) \([]\) \(16796160\) \(2.5695\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 194398k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 194398k do not have complex multiplication.

Modular form 194398.2.a.k

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