Properties

Label 208725.w
Number of curves $1$
Conductor $208725$
CM no
Rank $1$

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

Elliptic curves in class 208725.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
208725.w1 208725o1 \([1, 0, 0, -2308138, -1335202483]\) \(78605490625/985527\) \(17050011695771484375\) \([]\) \(6177600\) \(2.4997\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 208725.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 208725.w do not have complex multiplication.

Modular form 208725.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} - 3 q^{7} + 3 q^{8} + q^{9} - q^{12} + q^{13} + 3 q^{14} - q^{16} - 4 q^{17} - q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display