Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 273273.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273273.j1 273273j1 \([1, 1, 1, -38353624, -91287904492]\) \(2082918901/3993\) \(11961065843427715875861\) \([]\) \(30506112\) \(3.1256\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 273273.j1 has rank \(1\).

Complex multiplication

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

Modular form 273273.2.a.j

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