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	33600hk	Isogeny class
Conductor	33600	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	-379243855872000 = -1 · 220 · 310 · 53 · 72	Discriminant
Eigenvalues	2- 3- 5- 7- -2  2 -8 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4513,-945697]	[a1,a2,a3,a4,a6]
Generators	[167:1728:1]	Generators of the group modulo torsion
j	-310288733/11573604	j-invariant
L	6.8602697558786	L(r)(E,1)/r!
Ω	0.23363747647801	Real period
R	0.73407206105103	Regulator
r	1	Rank of the group of rational points
S	0.99999999999995	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33600bf2 8400bt2 100800pl2 33600fl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600hk2

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	2	-8	-2	0	6	-6	8	6	-8	4	-2	-8	-10	12	14	10	-4	-16	10	-10

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Quadratic twists for elliptic curve 33600hk2

-4	8	-3	5
33600bf2	8400bt2	100800pl2	33600fl2

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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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