Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 66270.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66270.p1 66270o1 \([1, 1, 1, 189, 9633]\) \(7189057/384000\) \(-39868032000\) \([]\) \(80640\) \(0.71376\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66270.p1 has rank \(1\).

Complex multiplication

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

Modular form 66270.2.a.p

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