Cremona's table of elliptic curves

3300 = 2² · 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 11+	Signs for the Atkin-Lehner involutions
Class	3300k	Isogeny class
Conductor	3300	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-15468750000 = -1 · 24 · 32 · 510 · 11	Discriminant
Eigenvalues	2- 3- 5+  2 11+ -2 -8 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-533,-7812]	[a1,a2,a3,a4,a6]
Generators	[43:225:1]	Generators of the group modulo torsion
j	-67108864/61875	j-invariant
L	4.1431233466259	L(r)(E,1)/r!
Ω	0.47852892816748	Real period
R	1.4430069262799	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	13200bs1 52800bb1 9900p1 660a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3300k1

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	-8	0	0	-2	0	-6	-8	-6	-4	10	12	8	-10	-14	-4	10	18

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Quadratic twists for elliptic curve 3300k1

-4	8	-3	5	-11
13200bs1	52800bb1	9900p1	660a1	36300bo1

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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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