Properties

Label 180336bg
Number of curves $1$
Conductor $180336$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bg1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 180336bg1 has rank \(0\).

L-function data

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

Complex multiplication

The elliptic curves in class 180336bg do not have complex multiplication.

Modular form 180336.2.a.bg

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

Elliptic curves in class 180336bg

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
180336.p1 180336bg1 \([0, -1, 0, -99145036008, -12170496618713232]\) \(-3772118414306118217515625/56562751486929272832\) \(-1616150669592087302957232713367552\) \([]\) \(1091171520\) \(5.1754\) \(\Gamma_0(N)\)-optimal