Properties

Label 497576.d
Number of curves 11
Conductor 497576497576
CM no
Rank 11

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Copy content sage:E = EllipticCurve("d1") E.isogeny_class()
 

Elliptic curves in class 497576.d

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
497576.d1 497576d1 [0,1,0,15689,678875][0, 1, 0, -15689, 678875] 351232/37351232/37 4499298737075244992987370752 [][] 10976001097600 1.35451.3545 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curve 497576.d1 has rank 11.

Complex multiplication

The elliptic curves in class 497576.d do not have complex multiplication.

Modular form 497576.2.a.d

Copy content sage:E.q_eigenform(10)
 
q+q32q5q72q9q11+6q132q15+4q17+8q19+O(q20)q + q^{3} - 2 q^{5} - q^{7} - 2 q^{9} - q^{11} + 6 q^{13} - 2 q^{15} + 4 q^{17} + 8 q^{19} + O(q^{20}) Copy content Toggle raw display