Properties

Label 200277.k
Number of curves $1$
Conductor $200277$
CM no
Rank $1$

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

Elliptic curves in class 200277.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
200277.k1 200277i1 \([1, -1, 1, -391505, 77613194]\) \(4515625/847\) \(1244801641752940887\) \([]\) \(2056320\) \(2.1900\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 200277.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 200277.k do not have complex multiplication.

Modular form 200277.2.a.k

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