Properties

Label 66654p
Number of curves $1$
Conductor $66654$
CM no
Rank $1$

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

Elliptic curves in class 66654p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66654.b1 66654p1 \([1, -1, 0, -4651596, 12172558608]\) \(-194975262337/1008189504\) \(-57556236474579761464896\) \([]\) \(6782976\) \(3.0515\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66654p1 has rank \(1\).

Complex multiplication

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

Modular form 66654.2.a.p

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