Properties

Label 409101bf
Number of curves $1$
Conductor $409101$
CM no
Rank $2$

Related objects

Downloads

Learn more

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

Elliptic curves in class 409101bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
409101.bf1 409101bf1 \([0, 1, 1, 39527, -30211604]\) \(1605632000/93710763\) \(-398600413559514243\) \([]\) \(2956800\) \(2.0569\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 409101bf1 has rank \(2\).

Complex multiplication

The elliptic curves in class 409101bf do not have complex multiplication.

Modular form 409101.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{9} - 2 q^{12} + 3 q^{13} + 4 q^{16} - 2 q^{17} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display