Properties

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

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Show commands: SageMath
E = EllipticCurve("hc1")
 
E.isogeny_class()
 

Elliptic curves in class 139650hc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.eh1 139650hc1 \([1, 0, 1, -1660146, -823460732]\) \(-172041783999846385/1179967488\) \(-3470549874892800\) \([]\) \(2515968\) \(2.1626\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 139650hc1 has rank \(0\).

Complex multiplication

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

Modular form 139650.2.a.hc

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 5 q^{11} + q^{12} + 4 q^{13} + q^{16} + 2 q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display