Properties

Label 409101.bi
Number of curves $1$
Conductor $409101$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("409101.bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 409101.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
409101.bi1 409101bi1 [1, 1, 0, -338990698, 2402218755721] [] 75018240 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101.bi1 has rank \(1\).

Modular form 409101.2.a.bi

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - 3q^{8} + q^{9} - q^{10} + q^{12} + q^{13} + q^{15} - q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)