Properties

Label 195195bk
Number of curves $1$
Conductor $195195$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 195195bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
195195.r1 195195bk1 \([0, -1, 1, 1309, 66536]\) \(112818618368/947244375\) \(-2081095891875\) \([]\) \(269568\) \(1.0450\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 195195bk1 has rank \(1\).

Complex multiplication

The elliptic curves in class 195195bk do not have complex multiplication.

Modular form 195195.2.a.bk

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