Properties

Label 139587r
Number of curves $1$
Conductor $139587$
CM no
Rank $1$

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

Elliptic curves in class 139587r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139587.r1 139587r1 \([0, -1, 1, -27840, -2077153]\) \(-98867482624/20696067\) \(-499552745241123\) \([]\) \(1555200\) \(1.5421\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 139587r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 139587r do not have complex multiplication.

Modular form 139587.2.a.r

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} + q^{7} + q^{9} - 8 q^{10} + 5 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 4 q^{15} - 4 q^{16} + 2 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display