Cremona's table of elliptic curves

8700 = 2² · 3 · 5² · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 29+	Signs for the Atkin-Lehner involutions
Class	8700l	Isogeny class
Conductor	8700	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	-19026900000000 = -1 · 28 · 38 · 58 · 29	Discriminant
Eigenvalues	2- 3- 5+ -2 -4 -2  8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,492,209988]	[a1,a2,a3,a4,a6]
Generators	[-12:450:1]	Generators of the group modulo torsion
j	3286064/4756725	j-invariant
L	4.7277516033699	L(r)(E,1)/r!
Ω	0.53789122924917	Real period
R	0.36622580817201	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	34800bt2 26100w2 1740b2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 8700l2

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	-4	-2	8	-4	6	+	0	-4	6	0	0	2	0	-6	-2	-8	4	-16	10	6	-8

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Quadratic twists for elliptic curve 8700l2

-4	-3	5
34800bt2	26100w2	1740b2

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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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