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	2800v	Isogeny class
Conductor	2800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-117440512000000 = -1 · 230 · 56 · 7	Discriminant
Eigenvalues	2- -2 5+ 7-  0  4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-68208,6853588]	[a1,a2,a3,a4,a6]
Generators	[148:150:1]	Generators of the group modulo torsion
j	-548347731625/1835008	j-invariant
L	2.4357724410939	L(r)(E,1)/r!
Ω	0.5927777031021	Real period
R	2.0545412119477	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	350d5 11200co5 25200eh5 112c5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2800v5

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
-	-2	+	-	0	4	-6	-2	0	-6	4	-2	6	8	-12	-6	6	8	-4	0	-2	-8	-6	-6	10

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Quadratic twists for elliptic curve 2800v5

-4	8	-3	5	-7
350d5	11200co5	25200eh5	112c5	19600cp5

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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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