Properties

Label 122018be
Number of curves $1$
Conductor $122018$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 122018be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122018.be1 122018be1 \([1, 0, 0, -61071280, -192774653696]\) \(-110931033861649/6497214464\) \(-1475397088211685157216256\) \([]\) \(18869760\) \(3.3936\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 122018be1 has rank \(1\).

Complex multiplication

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

Modular form 122018.2.a.be

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 3 q^{7} + q^{8} - 2 q^{9} + q^{10} + 4 q^{11} + q^{12} + 3 q^{14} + q^{15} + q^{16} - 3 q^{17} - 2 q^{18} + O(q^{20})\) Copy content Toggle raw display