Properties

Label 6034.a
Number of curves $1$
Conductor $6034$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 6034.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6034.a1 6034b1 \([1, -1, 0, -40, 112]\) \(-7177888089/337904\) \(-337904\) \([]\) \(1216\) \(-0.17619\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6034.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 6034.a do not have complex multiplication.

Modular form 6034.2.a.a

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