Properties

Label 17661e
Number of curves $1$
Conductor $17661$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 17661e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17661.i1 17661e1 \([1, 0, 1, -18, 19]\) \(707281/189\) \(158949\) \([]\) \(1440\) \(-0.29365\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 17661e1 has rank \(1\).

Complex multiplication

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

Modular form 17661.2.a.e

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