Properties

Label 8085q
Number of curves $1$
Conductor $8085$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 8085q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8085.o1 8085q1 \([0, 1, 1, -65, 179]\) \(12845056/165\) \(396165\) \([]\) \(960\) \(-0.11735\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8085q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 8085q do not have complex multiplication.

Modular form 8085.2.a.q

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