Properties

Label 2299.d
Number of curves 11
Conductor 22992299
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 2299.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2299.d1 2299a1 [0,0,1,1331,40263][0, 0, 1, 1331, -40263] 110592/361110592/361 851219116451-851219116451 [][] 95049504 0.972310.97231 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2299.d1 has rank 11.

Complex multiplication

The elliptic curves in class 2299.d do not have complex multiplication.

Modular form 2299.2.a.d

sage: E.q_eigenform(10)
 
q+2q23q3+2q43q56q6+2q7+6q96q106q12+2q13+4q14+9q154q16+6q17+12q18q19+O(q20)q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{5} - 6 q^{6} + 2 q^{7} + 6 q^{9} - 6 q^{10} - 6 q^{12} + 2 q^{13} + 4 q^{14} + 9 q^{15} - 4 q^{16} + 6 q^{17} + 12 q^{18} - q^{19} + O(q^{20}) Copy content Toggle raw display