Properties

Label 388416fz
Number of curves $1$
Conductor $388416$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fz1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 388416fz1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(7\)\(1 - T\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + T + 5 T^{2}\) 1.5.b
\(11\) \( 1 - T + 11 T^{2}\) 1.11.ab
\(13\) \( 1 - T + 13 T^{2}\) 1.13.ab
\(19\) \( 1 - 5 T + 19 T^{2}\) 1.19.af
\(23\) \( 1 + T + 23 T^{2}\) 1.23.b
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 388416fz do not have complex multiplication.

Modular form 388416.2.a.fz

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

Elliptic curves in class 388416fz

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388416.fz1 388416fz1 \([0, 1, 0, -109960261, -443851522909]\) \(-371806976516936704/89266779\) \(-35302326886731792384\) \([]\) \(24772608\) \(3.1288\) \(\Gamma_0(N)\)-optimal