Properties

Label 208b
Number of curves $1$
Conductor $208$
CM no
Rank $1$

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

Elliptic curves in class 208b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
208.b1 208b1 \([0, -1, 0, -16, 32]\) \(-235298/13\) \(-26624\) \([]\) \(16\) \(-0.39303\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 208b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 208b do not have complex multiplication.

Modular form 208.2.a.b

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