Properties

Label 406503.w
Number of curves $1$
Conductor $406503$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 406503.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
406503.w1 406503w1 \([0, 0, 1, -106671, 5086813]\) \(207474688/102789\) \(66503473966539261\) \([]\) \(6854400\) \(1.9210\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 406503.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 406503.w do not have complex multiplication.

Modular form 406503.2.a.w

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + 3 q^{5} - 3 q^{7} + 6 q^{10} - 5 q^{11} - 2 q^{13} - 6 q^{14} - 4 q^{16} - 6 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display