Properties

Label 194579.f
Number of curves $1$
Conductor $194579$
CM no
Rank $1$

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

Elliptic curves in class 194579.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
194579.f1 194579f1 \([0, 0, 1, 35378, 588159]\) \(884736/539\) \(-2983311560181491\) \([]\) \(1257984\) \(1.6585\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 194579.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 194579.f do not have complex multiplication.

Modular form 194579.2.a.f

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