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	8400d	Isogeny class
Conductor	8400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	595213920000000 = 211 · 312 · 57 · 7	Discriminant
Eigenvalues	2+ 3+ 5+ 7+ -4  2  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-43408,-3262688]	[a1,a2,a3,a4,a6]
Generators	[-118:450:1]	Generators of the group modulo torsion
j	282678688658/18600435	j-invariant
L	3.412351264229	L(r)(E,1)/r!
Ω	0.33212161242466	Real period
R	2.5686007298027	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	4200ba3 33600ge4 25200bd4 1680g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8400d3

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

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Quadratic twists for elliptic curve 8400d3

-4	8	-3	5	-7
4200ba3	33600ge4	25200bd4	1680g3	58800dn4

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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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