Properties

Label 1664.t
Number of curves $1$
Conductor $1664$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("t1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 1664.t1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(13\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 - 3 T + 3 T^{2}\) 1.3.ad
\(5\) \( 1 - 3 T + 5 T^{2}\) 1.5.ad
\(7\) \( 1 + T + 7 T^{2}\) 1.7.b
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(17\) \( 1 + 7 T + 17 T^{2}\) 1.17.h
\(19\) \( 1 - 6 T + 19 T^{2}\) 1.19.ag
\(23\) \( 1 + 6 T + 23 T^{2}\) 1.23.g
\(29\) \( 1 + 29 T^{2}\) 1.29.a
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 1664.t do not have complex multiplication.

Modular form 1664.2.a.t

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

Elliptic curves in class 1664.t

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1664.t1 1664i1 \([0, 0, 0, -1, 2]\) \(-864/13\) \(-1664\) \([]\) \(160\) \(-0.70052\) \(\Gamma_0(N)\)-optimal