Cremona's table of elliptic curves

6624 = 2⁵ · 3² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 23+	Signs for the Atkin-Lehner involutions
Class	6624f	Isogeny class
Conductor	6624	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	8192	Modular degree for the optimal curve
Δ	-7040530368 = -1 · 26 · 314 · 23	Discriminant
Eigenvalues	2- 3- -4 -4 -6  6  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-417,-5200]	[a1,a2,a3,a4,a6]
Generators	[31:108:1]	Generators of the group modulo torsion
j	-171879616/150903	j-invariant
L	2.3868504461016	L(r)(E,1)/r!
Ω	0.50954958047707	Real period
R	2.3421179582435	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	6624j1 13248bj1 2208c1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 6624f1

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

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Quadratic twists for elliptic curve 6624f1

-4	8	-3
6624j1	13248bj1	2208c1

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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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