Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 47190p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.j1 47190p1 \([1, 1, 0, -2, 114]\) \(-121/390\) \(-5709990\) \([]\) \(13440\) \(-0.024579\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47190p1 has rank \(1\).

Complex multiplication

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

Modular form 47190.2.a.p

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