Properties

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

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 273273.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273273.ba1 273273ba1 \([0, 1, 1, -20505, -1108285]\) \(3407872/99\) \(27699768092997\) \([]\) \(998400\) \(1.3571\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 273273.ba1 has rank \(1\).

Complex multiplication

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

Modular form 273273.2.a.ba

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