Properties

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

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 17661h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17661.d1 17661h1 \([1, 0, 0, -32, -75]\) \(-4317433/189\) \(-158949\) \([]\) \(1800\) \(-0.23667\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 17661h1 has rank \(1\).

Complex multiplication

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

Modular form 17661.2.a.h

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