Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 222180.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
222180.q1 222180o1 \([0, 1, 0, -12868414501, -2288366760719785]\) \(-6218589009063615570313216/56094690913037211867075\) \(-2125831023997871449298892148396800\) \([]\) \(1166989824\) \(5.0775\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 222180.q1 has rank \(1\).

Complex multiplication

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

Modular form 222180.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} + 5 q^{11} + 4 q^{13} - q^{15} - 2 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display