Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("409101.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 409101.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
409101.k1 409101k1 [1, 0, 0, -5629, 15911468] [] 3250368 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101.k1 has rank \(1\).

Modular form 409101.2.a.k

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