Properties

Label 66654.r
Number of curves $1$
Conductor $66654$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 66654.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66654.r1 66654f1 \([1, -1, 0, -2928114, -1934371148]\) \(-25727239787761/101406816\) \(-10943637306612960096\) \([]\) \(1520640\) \(2.5108\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66654.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 66654.r do not have complex multiplication.

Modular form 66654.2.a.r

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