Cremona's table of elliptic curves

8400 = 2⁴ · 3 · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	8400y	Isogeny class
Conductor	8400	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-11340000000000 = -1 · 211 · 34 · 510 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,5592,-16812]	[a1,a2,a3,a4,a6]
Generators	[18:300:1]	Generators of the group modulo torsion
j	604223422/354375	j-invariant
L	5.2334818218547	L(r)(E,1)/r!
Ω	0.42188588700639	Real period
R	0.77531063242456	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	4200a4 33600ev3 25200bm3 1680a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8400y4

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
+	-	+	-	0	-2	-2	-4	0	2	-4	-2	-2	8	-4	2	-12	-14	8	8	2	-8	-4	-18	2

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Quadratic twists for elliptic curve 8400y4

-4	8	-3	5	-7
4200a4	33600ev3	25200bm3	1680a4	58800o3

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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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