Properties

Label 211185.be
Number of curves $1$
Conductor $211185$
CM no
Rank $1$

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

Elliptic curves in class 211185.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
211185.be1 211185bb1 \([0, 0, 1, -215517, -60498095]\) \(-32278933504/27421875\) \(-940472889406171875\) \([]\) \(4402944\) \(2.1464\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 211185.be1 has rank \(1\).

Complex multiplication

The elliptic curves in class 211185.be do not have complex multiplication.

Modular form 211185.2.a.be

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + q^{5} - q^{7} + 2 q^{10} - 5 q^{11} + q^{13} - 2 q^{14} - 4 q^{16} + 7 q^{17} + O(q^{20})\) Copy content Toggle raw display