Properties

Label 272734j
Number of curves $1$
Conductor $272734$
CM no
Rank $1$

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

Elliptic curves in class 272734j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272734.j1 272734j1 \([1, 1, 0, -990266, 162401716]\) \(25248276104737/11918987872\) \(50697628990493168992\) \([]\) \(6912000\) \(2.4752\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 272734j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 272734j do not have complex multiplication.

Modular form 272734.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} - q^{8} - 2 q^{9} + 2 q^{10} - q^{12} - 5 q^{13} + 2 q^{15} + q^{16} + 2 q^{17} + 2 q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display