Properties

Label 17661.g
Number of curves $1$
Conductor $17661$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 17661.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17661.g1 17661b1 \([1, 1, 0, -26929, -1775330]\) \(-4317433/189\) \(-94546572049629\) \([]\) \(52200\) \(1.4470\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 17661.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 17661.g do not have complex multiplication.

Modular form 17661.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} + 2 q^{5} - q^{6} + q^{7} - 3 q^{8} + q^{9} + 2 q^{10} - q^{11} + q^{12} + 4 q^{13} + q^{14} - 2 q^{15} - q^{16} + q^{17} + q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display