Properties

Label 257139b
Number of curves $1$
Conductor $257139$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 257139b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
257139.b1 257139b1 \([0, 0, 1, -39, -239]\) \(-8998912/28571\) \(-20828259\) \([]\) \(127200\) \(0.090814\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 257139b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 257139b do not have complex multiplication.

Modular form 257139.2.a.b

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + 2 q^{5} - 4 q^{7} + 4 q^{10} + 6 q^{11} - 2 q^{13} - 8 q^{14} - 4 q^{16} + 4 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display