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	33600fe	Isogeny class
Conductor	33600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	207360	Modular degree for the optimal curve
Δ	-3870720000000000 = -1 · 221 · 33 · 510 · 7	Discriminant
Eigenvalues	2- 3+ 5+ 7-  6 -1 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,39167,229537]	[a1,a2,a3,a4,a6]
Generators	[1493:58176:1]	Generators of the group modulo torsion
j	2595575/1512	j-invariant
L	5.0837406969438	L(r)(E,1)/r!
Ω	0.2662894262939	Real period
R	4.7727586931422	Regulator
r	1	Rank of the group of rational points
S	0.99999999999993	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	33600co1 8400cj1 100800of1 33600hd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 33600fe1

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
-	+	+	-	6	-1	-3	-4	-3	-3	-5	-10	9	1	0	9	9	-11	4	12	10	10	-9	-6	-14

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Quadratic twists for elliptic curve 33600fe1

-4	8	-3	5
33600co1	8400cj1	100800of1	33600hd1

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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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