Properties

Label 47190.s
Number of curves $1$
Conductor $47190$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47190.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.s1 47190q1 \([1, 1, 0, 18696918, -27118513836]\) \(3372036481719478199/3434349802291200\) \(-736183380581712868147200\) \([]\) \(7717248\) \(3.2665\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 47190.s1 has rank \(1\).

Complex multiplication

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

Modular form 47190.2.a.s

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