Properties

Label 271950.k
Number of curves $1$
Conductor $271950$
CM no
Rank $0$

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

Elliptic curves in class 271950.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
271950.k1 271950k1 \([1, 1, 0, -2088650, -1316515500]\) \(-548166867106321/89547696000\) \(-164612451354750000000\) \([]\) \(11612160\) \(2.6067\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 271950.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 271950.k do not have complex multiplication.

Modular form 271950.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4 q^{11} - q^{12} + q^{13} + q^{16} - 6 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display