Properties

Label 121242j
Number of curves $1$
Conductor $121242$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 121242j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121242.i1 121242j1 \([1, 0, 1, 713776, -252518290]\) \(187615592384231/237141728784\) \(-50833435620543730704\) \([]\) \(3598848\) \(2.4673\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 121242j1 has rank \(1\).

Complex multiplication

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

Modular form 121242.2.a.j

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