Properties

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

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 121242.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121242.n1 121242e1 \([1, 0, 1, -388, -2686]\) \(4835382371/513024\) \(682834944\) \([]\) \(63360\) \(0.42968\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 121242.n1 has rank \(2\).

Complex multiplication

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

Modular form 121242.2.a.n

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