Properties

Label 215985.bf
Number of curves $1$
Conductor $215985$
CM no
Rank $2$

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

Elliptic curves in class 215985.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215985.bf1 215985bf1 \([0, -1, 1, -4275, -157642]\) \(-4878401536/3346875\) \(-5929193221875\) \([]\) \(336000\) \(1.1513\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 215985.bf1 has rank \(2\).

Complex multiplication

The elliptic curves in class 215985.bf do not have complex multiplication.

Modular form 215985.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} + q^{5} + q^{7} + q^{9} + 2 q^{12} - 3 q^{13} - q^{15} + 4 q^{16} - q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display