Properties

Label 121242a
Number of curves $1$
Conductor $121242$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 121242a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121242.b1 121242a1 \([1, 1, 0, -6052, 178468]\) \(13841287201/22044\) \(39052290684\) \([]\) \(176640\) \(0.93011\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 121242a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 121242a do not have complex multiplication.

Modular form 121242.2.a.a

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