Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 121242r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121242.e1 121242r1 \([1, 0, 1, -3456610, 2433177140]\) \(2578211650978275313/47984989814784\) \(85008336541268557824\) \([]\) \(6289920\) \(2.6183\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 121242r1 has rank \(2\).

Complex multiplication

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

Modular form 121242.2.a.r

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