Properties

Label 20286bc
Number of curves $1$
Conductor $20286$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 20286bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20286.bg1 20286bc1 \([1, -1, 0, -450, 769558]\) \(-49/1242\) \(-255758174999082\) \([]\) \(137088\) \(1.4435\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20286bc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 20286bc do not have complex multiplication.

Modular form 20286.2.a.bc

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 4 q^{5} - q^{8} - 4 q^{10} + 5 q^{11} - 2 q^{13} + q^{16} + 3 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display