Properties

Label 388080.gt
Number of curves $1$
Conductor $388080$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("gt1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 388080.gt1 has rank \(0\).

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 \(\mathbb{F}_p\)
\(13\) \( 1 - 3 T + 13 T^{2}\) 1.13.ad
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 - 8 T + 19 T^{2}\) 1.19.ai
\(23\) \( 1 + 6 T + 23 T^{2}\) 1.23.g
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 388080.2.a.gt

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

Elliptic curves in class 388080.gt

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.gt1 388080gt1 \([0, 0, 0, 1058757, 229218073]\) \(229651351304189696/172613560719655\) \(-98654864039468740080\) \([]\) \(11741184\) \(2.5247\) \(\Gamma_0(N)\)-optimal