Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("409101.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 409101.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
409101.z1 409101z1 [0, -1, 1, -4869685, 4187113545] [] 10881024 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101.z1 has rank \(1\).

Modular form 409101.2.a.z

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