Properties

Label 272816bf
Number of curves $1$
Conductor $272816$
CM no
Rank $1$

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

Elliptic curves in class 272816bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272816.bf1 272816bf1 \([0, 1, 0, -34776, 3171668]\) \(-47045881/17051\) \(-1685789446221824\) \([]\) \(884736\) \(1.6323\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 272816bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 272816bf do not have complex multiplication.

Modular form 272816.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 3 q^{7} - 2 q^{9} + 4 q^{11} - q^{15} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display