Cremona's table of elliptic curves

33600 = 2⁶ · 3 · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	33600gd	Isogeny class
Conductor	33600	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-2205000000 = -1 · 26 · 32 · 57 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+ -2  0  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8,-2262]	[a1,a2,a3,a4,a6]
Generators	[93:900:1]	Generators of the group modulo torsion
j	-64/2205	j-invariant
L	6.9670000896123	L(r)(E,1)/r!
Ω	0.66713124252339	Real period
R	2.6108056576917	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33600fa1 16800bd2 100800lj1 6720bs1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600gd1

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
-	-	+	+	-2	0	6	6	8	-6	-6	-10	2	-4	-8	-12	-12	10	-4	-2	-4	4	12	6	-16

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Quadratic twists for elliptic curve 33600gd1

-4	8	-3	5
33600fa1	16800bd2	100800lj1	6720bs1

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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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