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	33600cq	Isogeny class
Conductor	33600	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	398463045120000000 = 215 · 33 · 57 · 78	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-224033,27192063]	[a1,a2,a3,a4,a6]
Generators	[-293:8232:1]	Generators of the group modulo torsion
j	2428799546888/778248135	j-invariant
L	7.3339366303943	L(r)(E,1)/r!
Ω	0.27699271588144	Real period
R	0.55160420367137	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33600a3 16800g3 100800el3 6720a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600cq3

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

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Quadratic twists for elliptic curve 33600cq3

-4	8	-3	5
33600a3	16800g3	100800el3	6720a4

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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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