Properties

Label 163170fu
Number of curves $1$
Conductor $163170$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("fu1")
 
E.isogeny_class()
 

Elliptic curves in class 163170fu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163170.j1 163170fu1 \([1, -1, 0, -555, 9701]\) \(-19622547/29600\) \(-28548223200\) \([]\) \(109440\) \(0.69789\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 163170fu1 has rank \(1\).

Complex multiplication

The elliptic curves in class 163170fu do not have complex multiplication.

Modular form 163170.2.a.fu

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 3 q^{11} + q^{13} + q^{16} - q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display