Properties

Label 273273a
Number of curves $1$
Conductor $273273$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 273273a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273273.a1 273273a1 \([0, -1, 1, -251190, -79285438]\) \(-372736/363\) \(-1707016675243002123\) \([]\) \(11767392\) \(2.1945\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 273273a1 has rank \(0\).

Complex multiplication

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

Modular form 273273.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} - 4 q^{5} + 2 q^{6} + q^{9} + 8 q^{10} + q^{11} - 2 q^{12} + 4 q^{15} - 4 q^{16} - 6 q^{17} - 2 q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display