Properties

Label 28042.a
Number of curves 11
Conductor 2804228042
CM no
Rank 33

Related objects

Downloads

Learn more

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

Elliptic curves in class 28042.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28042.a1 28042b1 [1,1,0,19,49][1, -1, 0, -19, 49] 781229961/392588-781229961/392588 392588-392588 [][] 1641616416 0.22167-0.22167 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 28042.a1 has rank 33.

Complex multiplication

The elliptic curves in class 28042.a do not have complex multiplication.

Modular form 28042.2.a.a

sage: E.q_eigenform(10)
 
qq23q3+q44q5+3q6q7q8+6q9+4q106q113q123q13+q14+12q15+q166q176q184q19+O(q20)q - q^{2} - 3 q^{3} + q^{4} - 4 q^{5} + 3 q^{6} - q^{7} - q^{8} + 6 q^{9} + 4 q^{10} - 6 q^{11} - 3 q^{12} - 3 q^{13} + q^{14} + 12 q^{15} + q^{16} - 6 q^{17} - 6 q^{18} - 4 q^{19} + O(q^{20}) Copy content Toggle raw display