Properties

Label 20181o
Number of curves $1$
Conductor $20181$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 20181o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20181.c1 20181o1 \([0, 1, 1, -134, 728]\) \(-278966272/107163\) \(-102983643\) \([]\) \(10080\) \(0.24699\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20181o1 has rank \(2\).

Complex multiplication

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

Modular form 20181.2.a.o

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