Properties

Label 177744.q
Number of curves $1$
Conductor $177744$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 177744.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177744.q1 177744dc1 \([0, -1, 0, -8111, 137442]\) \(47104/21\) \(26312491054416\) \([]\) \(388608\) \(1.2706\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177744.q1 has rank \(0\).

Complex multiplication

The elliptic curves in class 177744.q do not have complex multiplication.

Modular form 177744.2.a.q

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