Properties

Label 1670.a
Number of curves $1$
Conductor $1670$
CM no
Rank $1$

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

Elliptic curves in class 1670.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1670.a1 1670a1 \([1, 1, 0, -38, -1132]\) \(-6321363049/534400000\) \(-534400000\) \([]\) \(1000\) \(0.35435\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1670.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1670.a do not have complex multiplication.

Modular form 1670.2.a.a

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