Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.u1 47190z1 \([1, 0, 1, -729, -8714]\) \(-24137569/4290\) \(-7599996690\) \([]\) \(40320\) \(0.62146\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47190z1 has rank \(1\).

Complex multiplication

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

Modular form 47190.2.a.z

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