Properties

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

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 222180.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
222180.w1 222180h1 \([0, 1, 0, -245, -1305]\) \(12058624/2205\) \(298609920\) \([]\) \(73728\) \(0.34483\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 222180.w1 has rank \(1\).

Complex multiplication

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

Modular form 222180.2.a.w

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