Properties

Label 850.i
Number of curves $1$
Conductor $850$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 850.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
850.i1 850f1 \([1, 1, 1, 1357, -2559]\) \(11053587253415/6565418768\) \(-164135469200\) \([]\) \(1344\) \(0.84133\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 850.i1 has rank \(0\).

Complex multiplication

The elliptic curves in class 850.i do not have complex multiplication.

Modular form 850.2.a.i

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