Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("409101.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 409101.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
409101.g1 409101g1 [1, 1, 1, -2801576, -1806095950] [] 6819840 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101.g1 has rank \(1\).

Modular form 409101.2.a.g

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