Properties

Label 66270.o
Number of curves $1$
Conductor $66270$
CM no
Rank $1$

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

Elliptic curves in class 66270.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66270.o1 66270n1 \([1, 1, 1, -16401871, -25072710571]\) \(20493730741489/460800000\) \(10972240893739468800000\) \([]\) \(7580160\) \(3.0163\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66270.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 66270.o do not have complex multiplication.

Modular form 66270.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 2 q^{7} + q^{8} + q^{9} - q^{10} + 5 q^{11} - q^{12} + 2 q^{13} - 2 q^{14} + q^{15} + q^{16} - 4 q^{17} + q^{18} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display