Properties

Label 177450kg
Number of curves $1$
Conductor $177450$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("kg1")
 
E.isogeny_class()
 

Elliptic curves in class 177450kg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.bg1 177450kg1 \([1, 1, 0, -30800, -2094750]\) \(-1223745654937/907578\) \(-2396573156250\) \([]\) \(645120\) \(1.3091\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177450kg1 has rank \(1\).

Complex multiplication

The elliptic curves in class 177450kg do not have complex multiplication.

Modular form 177450.2.a.kg

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 4 q^{11} - q^{12} + q^{14} + q^{16} - 7 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display