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Properties

Label 459186.b
Number of curves $1$
Conductor $459186$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("b1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 459186.b1 has rank \(0\).

Complex multiplication

The elliptic curves in class 459186.b do not have complex multiplication.

Modular form 459186.2.a.b

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

Elliptic curves in class 459186.b

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
459186.b1 459186b1 \([1, 1, 0, -2221657102, 65965921814530]\) \(-2038763327083572328197841/1980597708086151250278\) \(-1178105706288793040798662133238\) \([]\) \(1364912640\) \(4.4662\) \(\Gamma_0(N)\)-optimal