Properties

Label 269990.bf
Number of curves 11
Conductor 269990269990
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 269990.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
269990.bf1 269990bf1 [1,0,0,108046,13661626][1, 0, 0, -108046, 13661626] 1185664463338321/86093750-1185664463338321/86093750 10128843593750-10128843593750 [][] 11827201182720 1.54661.5466 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 269990.bf1 has rank 11.

Complex multiplication

The elliptic curves in class 269990.bf do not have complex multiplication.

Modular form 269990.2.a.bf

sage: E.q_eigenform(10)
 
q+q2+q3+q4q5+q6+q82q9q104q11+q122q13q15+q163q172q18+q19+O(q20)q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} - 2 q^{9} - q^{10} - 4 q^{11} + q^{12} - 2 q^{13} - q^{15} + q^{16} - 3 q^{17} - 2 q^{18} + q^{19} + O(q^{20}) Copy content Toggle raw display