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	2800w	Isogeny class
Conductor	2800	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-137200 = -1 · 24 · 52 · 73	Discriminant
Eigenvalues	2- -2 5+ 7- -3  4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-98,343]	[a1,a2,a3,a4,a6]
Generators	[7:7:1]	Generators of the group modulo torsion
j	-262885120/343	j-invariant
L	2.3955610734151	L(r)(E,1)/r!
Ω	3.2693754236063	Real period
R	0.24424247886596	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	700b2 11200cp2 25200eo2 2800ba2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2800w2

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	+	-	-3	4	0	-2	-3	9	-8	-5	-6	11	6	-6	0	-10	5	-15	10	7	12	-12	-8

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Quadratic twists for elliptic curve 2800w2

-4	8	-3	5	-7
700b2	11200cp2	25200eo2	2800ba2	19600cs2

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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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