Properties

Label 6069.a
Number of curves $1$
Conductor $6069$
CM no
Rank $1$

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

Elliptic curves in class 6069.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6069.a1 6069a1 \([0, -1, 1, -12234, 614882]\) \(-8390176768/1821771\) \(-43973123214699\) \([]\) \(32256\) \(1.3388\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6069.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6069.a do not have complex multiplication.

Modular form 6069.2.a.a

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