Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("409101.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 409101j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
409101.j1 409101j1 [1, 1, 1, -275822, -5457909346] [] 22752576 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101j1 has rank \(1\).

Modular form 409101.2.a.j

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