Cremona's table of elliptic curves

1600 = 2⁶ · 5²

Field	Data	Notes
Atkin-Lehner	2- 5-	Signs for the Atkin-Lehner involutions
Class	1600u	Isogeny class
Conductor	1600	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	8000000000 = 212 · 59	Discriminant
Eigenvalues	2-  0 5-  0  0 -4  8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-500,0]	[a1,a2,a3,a4,a6]
Generators	[-4:44:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	2.7625447192463	L(r)(E,1)/r!
Ω	1.1089953235983	Real period
R	2.4910336955099	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1600u2 800d1 14400ek2 1600t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1600u2

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
-	0	-	0	0	-4	8	0	0	-10	0	-12	-10	0	0	4	0	-10	0	0	16	0	0	-10	-8

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Quadratic twists for elliptic curve 1600u2

-4	8	-3	5	-7
1600u2	800d1	14400ek2	1600t2	78400jt2

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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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