Properties

Label 192027.r
Number of curves $1$
Conductor $192027$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 192027.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
192027.r1 192027t1 \([0, -1, 1, 1940, -6843]\) \(45056/27\) \(-483633249363\) \([]\) \(453024\) \(0.93134\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 192027.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 192027.r do not have complex multiplication.

Modular form 192027.2.a.r

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} + q^{7} + q^{9} - 8 q^{10} - 2 q^{12} + 2 q^{13} + 2 q^{14} + 4 q^{15} - 4 q^{16} + 4 q^{17} + 2 q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display