Properties

Label 123840fm
Number of curves $1$
Conductor $123840$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("fm1")
 
E.isogeny_class()
 

Elliptic curves in class 123840fm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123840.q1 123840fm1 \([0, 0, 0, -1398, 20122]\) \(-6476460544/1075\) \(-50155200\) \([]\) \(46080\) \(0.48557\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 123840fm1 has rank \(2\).

Complex multiplication

The elliptic curves in class 123840fm do not have complex multiplication.

Modular form 123840.2.a.fm

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} - 5 q^{11} - q^{13} + q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display