Properties

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

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 121242bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121242.bg1 121242bg1 \([1, 0, 0, -844, 11408]\) \(-49958012987/13851648\) \(-18436543488\) \([]\) \(92160\) \(0.68552\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 121242bg1 has rank \(1\).

Complex multiplication

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

Modular form 121242.2.a.bg

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