Properties

Label 47190j
Number of curves $1$
Conductor $47190$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.k1 47190j1 \([1, 1, 0, -442862, 163578804]\) \(-4073768343611/2555904000\) \(-6026687935217664000\) \([]\) \(1083456\) \(2.3052\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47190j1 has rank \(1\).

Complex multiplication

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

Modular form 47190.2.a.j

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