Properties

Label 16830.s
Number of curves $1$
Conductor $16830$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 16830.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16830.s1 16830w1 \([1, -1, 0, 45, 135]\) \(13651919/20570\) \(-14995530\) \([]\) \(3840\) \(0.062315\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 16830.s1 has rank \(1\).

Complex multiplication

The elliptic curves in class 16830.s do not have complex multiplication.

Modular form 16830.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + 4 q^{7} - q^{8} + q^{10} + q^{11} - q^{13} - 4 q^{14} + q^{16} - q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display