Properties

Label 139650hr
Number of curves $1$
Conductor $139650$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("hr1")
 
E.isogeny_class()
 

Elliptic curves in class 139650hr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.r1 139650hr1 \([1, 1, 0, -102435, -12665925]\) \(-23565848363/9234\) \(-46578150879750\) \([]\) \(770560\) \(1.5874\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 139650hr1 has rank \(0\).

Complex multiplication

The elliptic curves in class 139650hr do not have complex multiplication.

Modular form 139650.2.a.hr

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 3 q^{11} - q^{12} + q^{13} + q^{16} + 4 q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display