Properties

Label 19890k
Number of curves $1$
Conductor $19890$
CM no
Rank $0$

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

Elliptic curves in class 19890k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19890.g1 19890k1 \([1, -1, 0, 161640, -63854784]\) \(640680045567719039/2783963520000000\) \(-2029509406080000000\) \([]\) \(419328\) \(2.1954\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19890k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 19890k do not have complex multiplication.

Modular form 19890.2.a.k

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