Properties

Label 164738.bd
Number of curves $1$
Conductor $164738$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 164738.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
164738.bd1 164738f1 \([1, 1, 1, -1731465, -93776201]\) \(1027243729/587776\) \(328475686860350224384\) \([]\) \(7096320\) \(2.6265\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 164738.bd1 has rank \(1\).

Complex multiplication

The elliptic curves in class 164738.bd do not have complex multiplication.

Modular form 164738.2.a.bd

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} - 2 q^{9} + q^{10} + 6 q^{11} - q^{12} - 4 q^{13} - q^{15} + q^{16} + 7 q^{17} - 2 q^{18} + O(q^{20})\) Copy content Toggle raw display