Properties

Label 189618.k
Number of curves $1$
Conductor $189618$
CM no
Rank $0$

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

Elliptic curves in class 189618.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.k1 189618br1 \([1, 1, 0, 727711, -49803723]\) \(309147739823/186772608\) \(-25748190057584472192\) \([]\) \(5031936\) \(2.4138\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 189618.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 189618.k do not have complex multiplication.

Modular form 189618.2.a.k

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