Cremona's table of elliptic curves

2800 = 2⁴ · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	2800t	Isogeny class
Conductor	2800	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-6860000000 = -1 · 28 · 57 · 73	Discriminant
Eigenvalues	2-  1 5+ 7- -3  1  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-20133,1092863]	[a1,a2,a3,a4,a6]
Generators	[103:350:1]	Generators of the group modulo torsion
j	-225637236736/1715	j-invariant
L	3.7889070316799	L(r)(E,1)/r!
Ω	1.1925230249929	Real period
R	0.26476826528517	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	700a2 11200cl2 25200em2 560f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2800t2

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	+	-	-3	1	3	-2	-6	-9	-8	10	0	2	-3	0	-12	8	8	0	-14	-5	-12	12	-17

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Quadratic twists for elliptic curve 2800t2

-4	8	-3	5	-7
700a2	11200cl2	25200em2	560f2	19600cj2

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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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