Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 222180.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
222180.b1 222180y1 \([0, -1, 0, -595301, 177229185]\) \(-615640662016/978075\) \(-37066291746220800\) \([]\) \(2787840\) \(2.0773\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 222180.b1 has rank \(1\).

Complex multiplication

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

Modular form 222180.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + q^{11} + 4q^{13} + q^{15} - 6q^{17} - 7q^{19} + O(q^{20})\)  Toggle raw display