Properties

Label 1682.f
Number of curves 11
Conductor 16821682
CM no
Rank 00

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 1682.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1682.f1 1682h1 [1,1,1,221025,19814919][1, -1, 1, 221025, 19814919] 2838375/20482838375/2048 861608413798811648-861608413798811648 [][] 4785047850 2.12982.1298 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1682.f1 has rank 00.

Complex multiplication

The elliptic curves in class 1682.f do not have complex multiplication.

Modular form 1682.2.a.f

sage: E.q_eigenform(10)
 
q+q23q3+q43q6+4q7+q8+6q9+q113q12+6q13+4q14+q162q17+6q18q19+O(q20)q + q^{2} - 3 q^{3} + q^{4} - 3 q^{6} + 4 q^{7} + q^{8} + 6 q^{9} + q^{11} - 3 q^{12} + 6 q^{13} + 4 q^{14} + q^{16} - 2 q^{17} + 6 q^{18} - q^{19} + O(q^{20}) Copy content Toggle raw display