Properties

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

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

Elliptic curves in class 6069.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6069.d1 6069e1 \([0, 1, 1, 1030189, 364409024]\) \(5009339741732864/5271114033171\) \(-127231878682533301299\) \([]\) \(156672\) \(2.5444\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6069.d1 has rank \(1\).

Complex multiplication

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

Modular form 6069.2.a.d

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