Properties

Label 277725.bd
Number of curves $1$
Conductor $277725$
CM no
Rank $2$

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

Elliptic curves in class 277725.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277725.bd1 277725bd1 \([0, -1, 1, -1533, -25657]\) \(-48234496/7875\) \(-65091796875\) \([]\) \(221184\) \(0.80246\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 277725.bd1 has rank \(2\).

Complex multiplication

The elliptic curves in class 277725.bd do not have complex multiplication.

Modular form 277725.2.a.bd

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