Properties

Label 409101bf
Number of curves $1$
Conductor $409101$
CM no
Rank $2$

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Show commands for: SageMath
sage: E = EllipticCurve("409101.bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 409101bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
409101.bf1 409101bf1 [0, 1, 1, 39527, -30211604] [] 2956800 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101bf1 has rank \(2\).

Modular form 409101.2.a.bf

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