Properties

Label 19890.a
Number of curves $1$
Conductor $19890$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 19890.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19890.a1 19890j1 \([1, -1, 0, -12690, -547700]\) \(-310027558782241/414375000\) \(-302079375000\) \([]\) \(64512\) \(1.1088\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19890.a1 has rank \(1\).

Complex multiplication

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

Modular form 19890.2.a.a

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