Properties

Label 16650.r
Number of curves $1$
Conductor $16650$
CM no
Rank $2$

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

Elliptic curves in class 16650.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16650.r1 16650bj1 \([1, -1, 0, -117, 39541]\) \(-625/2368\) \(-674325000000\) \([]\) \(25920\) \(0.94869\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 16650.r1 has rank \(2\).

Complex multiplication

The elliptic curves in class 16650.r do not have complex multiplication.

Modular form 16650.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} - 4 q^{11} - 2 q^{13} + q^{16} - 8 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display