Properties

Label 170e
Number of curves $1$
Conductor $170$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 170e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
170.d1 170e1 \([1, -1, 0, -10, -10]\) \(-116930169/170\) \(-170\) \([]\) \(20\) \(-0.66997\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 170e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 170e do not have complex multiplication.

Modular form 170.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + 3 q^{3} + q^{4} - q^{5} - 3 q^{6} + 2 q^{7} - q^{8} + 6 q^{9} + q^{10} - 4 q^{11} + 3 q^{12} - 3 q^{13} - 2 q^{14} - 3 q^{15} + q^{16} + q^{17} - 6 q^{18} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display