Properties

Label 8085.a
Number of curves $1$
Conductor $8085$
CM no
Rank $0$

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

Elliptic curves in class 8085.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8085.a1 8085i1 \([0, -1, 1, -85486, 9555342]\) \(1409995418369929216/15792626953125\) \(773838720703125\) \([]\) \(63360\) \(1.6708\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8085.a1 has rank \(0\).

Complex multiplication

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

Modular form 8085.2.a.a

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