Properties

Label 8034.d
Number of curves $1$
Conductor $8034$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 8034.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8034.d1 8034e1 \([1, 1, 1, -29009, 1888175]\) \(2699746096571246737/2402493530112\) \(2402493530112\) \([]\) \(48960\) \(1.3006\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8034.d1 has rank \(2\).

Complex multiplication

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

Modular form 8034.2.a.d

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