Properties

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

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Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 47190cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.ch1 47190cf1 \([1, 1, 1, -305, -153163]\) \(-121/390\) \(-10115595594390\) \([]\) \(147840\) \(1.1744\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47190cf1 has rank \(1\).

Complex multiplication

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

Modular form 47190.2.a.cf

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