Properties

Label 273273.w
Number of curves $1$
Conductor $273273$
CM no
Rank $1$

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

Elliptic curves in class 273273.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273273.w1 273273w1 \([0, -1, 1, -5945, 173942]\) \(3407872/99\) \(675156198717\) \([]\) \(537600\) \(1.0476\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 273273.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 273273.w do not have complex multiplication.

Modular form 273273.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} - 4 q^{5} + q^{9} + q^{11} + 2 q^{12} + 4 q^{15} + 4 q^{16} + 2 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display