Properties

Label 40733h
Number of curves $1$
Conductor $40733$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 40733h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40733.h1 40733h1 \([1, -1, 0, -133936, 13676113]\) \(1794942305577/495598411\) \(73366351359372379\) \([]\) \(675840\) \(1.9437\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40733h1 has rank \(1\).

Complex multiplication

The elliptic curves in class 40733h do not have complex multiplication.

Modular form 40733.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} - q^{4} - 3 q^{5} - 3 q^{6} + q^{7} - 3 q^{8} + 6 q^{9} - 3 q^{10} - q^{11} + 3 q^{12} - q^{13} + q^{14} + 9 q^{15} - q^{16} - 4 q^{17} + 6 q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display