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	8624g	Isogeny class
Conductor	8624	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	133568512 = 211 · 72 · 113	Discriminant
Eigenvalues	2+ -1 -2 7- 11- -3  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-184,848]	[a1,a2,a3,a4,a6]
Generators	[2:22:1]	Generators of the group modulo torsion
j	6902546/1331	j-invariant
L	2.819237152679	L(r)(E,1)/r!
Ω	1.7530092375792	Real period
R	0.26803786808832	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	4312c1 34496cl1 77616bq1 8624a1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8624g1

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	-2	-	-	-3	2	4	4	-7	-8	12	8	-8	-10	14	-9	5	3	6	-4	17	-6	2	-7

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Quadratic twists for elliptic curve 8624g1

-4	8	-3	-7	-11
4312c1	34496cl1	77616bq1	8624a1	94864s1

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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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