Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.p1 47190n1 \([1, 1, 0, -6944797, -7479615491]\) \(-172806866567322361/12654720000000\) \(-2712651618568320000000\) \([]\) \(2882880\) \(2.8619\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47190n1 has rank \(1\).

Complex multiplication

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

Modular form 47190.2.a.n

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