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Properties

Label 451770.k
Number of curves $1$
Conductor $451770$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("k1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 451770.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 451770.k do not have complex multiplication.

Modular form 451770.2.a.k

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 3 q^{7} - q^{8} + q^{9} - q^{10} + q^{11} - q^{12} + q^{13} + 3 q^{14} - q^{15} + q^{16} - 5 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 451770.k

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
451770.k1 451770k1 \([1, 1, 0, -46725367, 122914067221]\) \(4397152681594331569/80019456000\) \(205308031493013504000\) \([]\) \(44914176\) \(3.0236\) \(\Gamma_0(N)\)-optimal