Properties

Label 18928f
Number of curves $1$
Conductor $18928$
CM no
Rank $2$

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

Elliptic curves in class 18928f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18928.f1 18928f1 \([0, 1, 0, -56, 196]\) \(-114244/49\) \(-8479744\) \([]\) \(3840\) \(0.036996\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 18928f1 has rank \(2\).

Complex multiplication

The elliptic curves in class 18928f do not have complex multiplication.

Modular form 18928.2.a.f

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + q^{7} + q^{9} + 2 q^{11} + 2 q^{15} - 3 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display