Properties

Label 216600.ek
Number of curves $1$
Conductor $216600$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ek1")
 
E.isogeny_class()
 

Elliptic curves in class 216600.ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
216600.ek1 216600dk1 \([0, 1, 0, -2105833, -1407432037]\) \(-8780800/2187\) \(-257223354367500000000\) \([]\) \(12065760\) \(2.6343\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 216600.ek1 has rank \(1\).

Complex multiplication

The elliptic curves in class 216600.ek do not have complex multiplication.

Modular form 216600.2.a.ek

sage: E.q_eigenform(10)
 
\(q + q^{3} + 5 q^{7} + q^{9} - 6 q^{11} - 3 q^{13} + 2 q^{17} + O(q^{20})\) Copy content Toggle raw display