Cremona's table of elliptic curves

8624 = 2⁴ · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	8624n	Isogeny class
Conductor	8624	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	1005708919570432 = 217 · 78 · 113	Discriminant
Eigenvalues	2- -1  0 7+ 11-  5  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4451568,3616561600]	[a1,a2,a3,a4,a6]
Generators	[1218:22:1]	Generators of the group modulo torsion
j	413160293352625/42592	j-invariant
L	3.6419366410524	L(r)(E,1)/r!
Ω	0.38039347304721	Real period
R	1.5956883679234	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	1078g2 34496ca2 77616ei2 8624z2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8624n2

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
-	-1	0	+	-	5	6	-2	-6	3	-8	2	-6	4	-6	-12	3	-7	13	12	-10	1	-6	6	-13

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Quadratic twists for elliptic curve 8624n2

-4	8	-3	-7	-11
1078g2	34496ca2	77616ei2	8624z2	94864bh2

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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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