Properties

Label 222180.o
Number of curves $1$
Conductor $222180$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 222180.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
222180.o1 222180m1 \([0, 1, 0, 177844, -7168956]\) \(4593495403625264/2824941065625\) \(-382564818871200000\) \([]\) \(2252160\) \(2.0630\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 222180.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 222180.o do not have complex multiplication.

Modular form 222180.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} + q^{11} + q^{13} - q^{15} - 2 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display