Cremona's table of elliptic curves

84700 = 2² · 5² · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	84700o	Isogeny class
Conductor	84700	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	462157747436000000 = 28 · 56 · 72 · 119	Discriminant
Eigenvalues	2-  2 5+ 7- 11+ -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-255108,-37195288]	[a1,a2,a3,a4,a6]
Generators	[-358:2850:1]	Generators of the group modulo torsion
j	194672/49	j-invariant
L	9.4016515909839	L(r)(E,1)/r!
Ω	0.21636012376519	Real period
R	3.6211430840273	Regulator
r	1	Rank of the group of rational points
S	1.0000000001068	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3388b2 84700d2	Quadratic twists by: 5 -11

Hecke Eigenvalues for elliptic curve 84700o2

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	+	-	+	-6	6	-4	0	-4	-2	6	2	4	-10	6	6	-14	12	-8	10	12	-4	10	-14

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Quadratic twists for elliptic curve 84700o2

5	-11
3388b2	84700d2

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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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