Properties

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

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 273273.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273273.c1 273273c1 \([0, 1, 1, -15500, -5258158]\) \(-1593413632/45196767\) \(-11682227706400251\) \([]\) \(2985984\) \(1.7636\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 273273.c1 has rank \(1\).

Complex multiplication

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

Modular form 273273.2.a.c

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