Properties

Label 32192e
Number of curves 11
Conductor 3219232192
CM no
Rank 33

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 32192e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32192.a1 32192e1 [0,0,0,52,160][0, 0, 0, -52, 160] 3796416/503-3796416/503 2060288-2060288 [][] 1868818688 0.055702-0.055702 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 32192e1 has rank 33.

Complex multiplication

The elliptic curves in class 32192e do not have complex multiplication.

Modular form 32192.2.a.e

sage: E.q_eigenform(10)
 
q3q34q53q7+6q93q117q13+12q152q172q19+O(q20)q - 3 q^{3} - 4 q^{5} - 3 q^{7} + 6 q^{9} - 3 q^{11} - 7 q^{13} + 12 q^{15} - 2 q^{17} - 2 q^{19} + O(q^{20}) Copy content Toggle raw display