Properties

Label 122018bg
Number of curves 11
Conductor 122018122018
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 122018bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122018.v1 122018bg1 [1,0,0,2990712,2115424336][1, 0, 0, -2990712, 2115424336] 77086633/5776-77086633/5776 221664225993342120976-221664225993342120976 [][] 80870408087040 2.65252.6525 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 122018bg1 has rank 11.

Complex multiplication

The elliptic curves in class 122018bg do not have complex multiplication.

Modular form 122018.2.a.bg

sage: E.q_eigenform(10)
 
q+q22q3+q43q52q6+q8+q93q106q112q12+6q15+q16+7q17+q18+O(q20)q + q^{2} - 2 q^{3} + q^{4} - 3 q^{5} - 2 q^{6} + q^{8} + q^{9} - 3 q^{10} - 6 q^{11} - 2 q^{12} + 6 q^{15} + q^{16} + 7 q^{17} + q^{18} + O(q^{20}) Copy content Toggle raw display