Properties

Label 333270.ej
Number of curves $1$
Conductor $333270$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ej1")
 
E.isogeny_class()
 

Elliptic curves in class 333270.ej

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.ej1 333270ej1 \([1, -1, 1, 75283, -9227339]\) \(826551/1120\) \(-63939353262230880\) \([]\) \(3179520\) \(1.9105\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 333270.ej1 has rank \(1\).

Complex multiplication

The elliptic curves in class 333270.ej do not have complex multiplication.

Modular form 333270.2.a.ej

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} + 4 q^{13} - q^{14} + q^{16} - q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display