Properties

Label 388080.k
Number of curves $1$
Conductor $388080$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("k1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 388080.k1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1 + T\)
\(7\)\(1\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 + 6 T + 13 T^{2}\) 1.13.g
\(17\) \( 1 - 8 T + 17 T^{2}\) 1.17.ai
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 7 T + 23 T^{2}\) 1.23.h
\(29\) \( 1 - 9 T + 29 T^{2}\) 1.29.aj
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 388080.k do not have complex multiplication.

Modular form 388080.2.a.k

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

Elliptic curves in class 388080.k

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.k1 388080k1 \([0, 0, 0, -71883, 8951418]\) \(-5729578281/1512500\) \(-10843638220800000\) \([]\) \(3064320\) \(1.7936\) \(\Gamma_0(N)\)-optimal