Properties

Label 20216.k
Number of curves $1$
Conductor $20216$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 20216.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20216.k1 20216h1 \([0, 1, 0, -43440, 994301]\) \(92416/49\) \(4806755946115984\) \([]\) \(54720\) \(1.7005\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20216.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 20216.k do not have complex multiplication.

Modular form 20216.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} - 2 q^{9} - q^{13} + q^{15} + 5 q^{17} + O(q^{20})\) Copy content Toggle raw display