Properties

Label 47190.x
Number of curves $1$
Conductor $47190$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.x1 47190w1 \([1, 0, 1, -69369, -7038308]\) \(-305088363822419089/15974400000\) \(-1932902400000\) \([]\) \(163200\) \(1.4260\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47190.x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 47190.x do not have complex multiplication.

Modular form 47190.2.a.x

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