Properties

Label 20181e
Number of curves $1$
Conductor $20181$
CM no
Rank $0$

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

Elliptic curves in class 20181e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20181.a1 20181e1 \([0, -1, 1, -129094, -22985136]\) \(-278966272/107163\) \(-91398362245289883\) \([]\) \(312480\) \(1.9640\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20181e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 20181e do not have complex multiplication.

Modular form 20181.2.a.e

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + q^{7} + q^{9} + 4 q^{10} + 2 q^{11} - 2 q^{12} + 7 q^{13} - 2 q^{14} + 2 q^{15} - 4 q^{16} + 2 q^{17} - 2 q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display