Properties

Label 38646.w
Number of curves $1$
Conductor $38646$
CM no
Rank $1$

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

Elliptic curves in class 38646.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38646.w1 38646bg1 \([1, -1, 1, -10490075408, -413535954256397]\) \(175118494194706007910209553147321/3389249508578689024\) \(2470762891753864298496\) \([]\) \(39866400\) \(4.0911\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 38646.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 38646.w do not have complex multiplication.

Modular form 38646.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + 4 q^{7} + q^{8} - q^{10} - 3 q^{11} - 5 q^{13} + 4 q^{14} + q^{16} + 8 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display