Properties

Label 8034.k
Number of curves $1$
Conductor $8034$
CM no
Rank $0$

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

Elliptic curves in class 8034.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8034.k1 8034h1 \([1, 0, 0, -751641, -250756767]\) \(46962924452705609230609/27478038929349528\) \(27478038929349528\) \([]\) \(213696\) \(2.0994\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8034.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 8034.k do not have complex multiplication.

Modular form 8034.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 4 q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + 4 q^{10} - 3 q^{11} + q^{12} - q^{13} - q^{14} + 4 q^{15} + q^{16} - 3 q^{17} + q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display