Properties

Label 409101d
Number of curves $1$
Conductor $409101$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("409101.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 409101d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
409101.d1 409101d1 [0, 1, 1, -962474, -10275428740] [] 44236800 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101d1 has rank \(1\).

Modular form 409101.2.a.d

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