Properties

Label 1477a
Number of curves $1$
Conductor $1477$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 1477a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1477.a1 1477a1 \([1, 0, 0, -6, 7]\) \(-24137569/10339\) \(-10339\) \([]\) \(104\) \(-0.52211\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1477a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 1477a do not have complex multiplication.

Modular form 1477.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} - q^{4} - q^{5} + 2 q^{6} - q^{7} + 3 q^{8} + q^{9} + q^{10} - 5 q^{11} + 2 q^{12} - 5 q^{13} + q^{14} + 2 q^{15} - q^{16} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display