Properties

Label 17787.x
Number of curves $1$
Conductor $17787$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 17787.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17787.x1 17787p1 \([1, 0, 1, 17663, 4994273]\) \(24167/441\) \(-11121626623929129\) \([]\) \(152064\) \(1.7594\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 17787.x1 has rank \(0\).

Complex multiplication

The elliptic curves in class 17787.x do not have complex multiplication.

Modular form 17787.2.a.x

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