Properties

Label 40080bf
Number of curves $1$
Conductor $40080$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 40080bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40080.bc1 40080bf1 \([0, 1, 0, 40, 660]\) \(1685159/45090\) \(-184688640\) \([]\) \(20736\) \(0.26630\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40080bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 40080bf do not have complex multiplication.

Modular form 40080.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 5 q^{7} + q^{9} - 6 q^{11} - 4 q^{13} + q^{15} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display