Cremona's table of elliptic curves

1600 = 2⁶ · 5²

Field	Data	Notes
Atkin-Lehner	2- 5-	Signs for the Atkin-Lehner involutions
Class	1600v	Isogeny class
Conductor	1600	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-1310720000 = -1 · 221 · 54	Discriminant
Eigenvalues	2-  1 5- -2 -3  4 -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8033,274463]	[a1,a2,a3,a4,a6]
Generators	[23:320:1]	Generators of the group modulo torsion
j	-349938025/8	j-invariant
L	3.0732407264865	L(r)(E,1)/r!
Ω	1.4120687224424	Real period
R	0.18136751406185	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1600j2 400c2 14400ew2 1600q4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1600v2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	1	-	-2	-3	4	-3	5	-6	0	-2	-2	-3	-4	-12	-6	0	-2	-13	-12	11	10	-9	15	2

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Quadratic twists for elliptic curve 1600v2

-4	8	-3	5	-7
1600j2	400c2	14400ew2	1600q4	78400kp2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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