Properties

Label 16650w
Number of curves $1$
Conductor $16650$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 16650w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16650.p1 16650w1 \([1, -1, 0, -41292, -205262384]\) \(-683565019129/1597684769280\) \(-18198628075080000000\) \([]\) \(414720\) \(2.3746\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 16650w1 has rank \(1\).

Complex multiplication

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

Modular form 16650.2.a.w

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