Properties

Label 66248p
Number of curves $1$
Conductor $66248$
CM no
Rank $2$

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

Elliptic curves in class 66248p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66248.f1 66248p1 \([0, -1, 0, -598992, -48838271]\) \(53385472/28561\) \(12715628346713712784\) \([]\) \(1354752\) \(2.3570\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 66248p1 has rank \(2\).

Complex multiplication

The elliptic curves in class 66248p do not have complex multiplication.

Modular form 66248.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} - 2 q^{9} + q^{11} + 3 q^{15} - 5 q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display