Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 177744.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177744.f1 177744bn1 \([0, -1, 0, 76988368, 174458073024]\) \(83228502970940543/69854999176704\) \(-42356928119675472813490176\) \([]\) \(50181120\) \(3.6050\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177744.f1 has rank \(1\).

Complex multiplication

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

Modular form 177744.2.a.f

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