Properties

Label 177744.bd
Number of curves $1$
Conductor $177744$
CM no
Rank $1$

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

Elliptic curves in class 177744.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177744.bd1 177744df1 \([0, -1, 0, 3320, 49168]\) \(162365474/137781\) \(-3433229162496\) \([]\) \(345600\) \(1.0930\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 177744.bd1 has rank \(1\).

Complex multiplication

The elliptic curves in class 177744.bd do not have complex multiplication.

Modular form 177744.2.a.bd

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} - 6 q^{11} + q^{13} - q^{15} - 2 q^{17} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display