Properties

Label 160016.b
Number of curves $1$
Conductor $160016$
CM no
Rank $3$

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

Elliptic curves in class 160016.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160016.b1 160016e1 \([0, 0, 0, -251, 1546]\) \(-853915554/10001\) \(-20482048\) \([]\) \(39296\) \(0.21572\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 160016.b1 has rank \(3\).

Complex multiplication

The elliptic curves in class 160016.b do not have complex multiplication.

Modular form 160016.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 3 q^{7} - 3 q^{9} - 2 q^{11} - 4 q^{13} - 6 q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display