Properties

Label 6699.b
Number of curves $1$
Conductor $6699$
CM no
Rank $1$

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

Elliptic curves in class 6699.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6699.b1 6699c1 \([1, 1, 1, 0, -12]\) \(-1/60291\) \(-60291\) \([]\) \(432\) \(-0.40387\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6699.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6699.b do not have complex multiplication.

Modular form 6699.2.a.b

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